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Saibian's xec_numbers article leak 2014-01-18

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  1. 4.3.3 - Forging Extended Cascading-E Numbers
  2. Leaked version (2014-01-18)
  3.  
  4. Copyright © Sbiis Saibian 2014, posted here with permission.
  5.  
  6.  
  7. The following is a leaked, unfinished draft of the article "Forging Extended Cascading-E Numbers" by Sbiis Saibian.
  8.  
  9.  
  10. Sbiis Saibian has written a web book, "One to Infinity: A Guide to the Finite", in which he introduces and describes various notations about googology (the mathematical study of large numbers) in great detail. He has invented his own notation called the Extensible-E System (ExE).
  11.  
  12. On 2014-01-17 (or earlier), Saibian accidnetally released an article about the numbers named with the new, un-released part of ExE, called "Extended Cascading-E Notation" (xE^). A user (Googleaarex) in Googology Wiki (googology.wikia.com) created a page with an analysis of the leaked article. On 2014-01-18, Saibian's wife reported the stolen information, resulting in Googleaarex's page being taken down and Saibian's article becoming private again.
  13.  
  14. Before it was taken down, I've saved the article on my computer, in plain-text. Today, I've decided to publish the article to the general public as it's the one-year anniversary of the incident.
  15.  
  16. The article has been officially released at 2014-01-30, and the content has since been refined and has been split into four articles. Currently, the link to the article below leads to the first of these four articles.
  17.  
  18.  
  19. === Links ===
  20. * The leaked article was located on: https://sites.google.com/site/largenumbers/home/4-3/xec_numbers
  21. * One to Infinity main page: https://sites.google.com/site/largenumbers/home
  22. * Saibian's wife's report about the stolen info: http://googology.wikia.com/wiki/User_talk:Googleaarex/xCE_levels
  23.  
  24. The permission for this post can be seen here:
  25. http://googology.wikia.com/wiki/User_talk:Sbiis_Saibian#Anniversary_of_the_xec_numbers_leak
  26. (my Wikia username is Cloudy176, with the signature "☁ I want more clouds! ⛅")
  27.  
  28.  
  29.  
  30. ===================================================================================
  31.  
  32.  
  33.  
  34.  
  35.  
  36.  
  37.  
  38.  
  39.  
  40.  
  41. Large Numbers
  42.  
  43.  
  44.  
  45.  
  46.  
  47.  
  48.  
  49.  
  50.  
  51. home‎ > ‎4.3‎ > ‎
  52.  
  53. xec_numbers
  54.  
  55.  
  56.  
  57.  
  58.  
  59.  
  60.  
  61.  
  62.  
  63. 4.3.3
  64.  
  65. Forging Extended Cascading-E Numbers
  66.  
  67.  
  68.  
  69.  
  70.  
  71.  
  72. Introduction
  73.  
  74.  
  75.  
  76.  
  77. Now that we have developed a powerful and well defined Extended Cascading-E Notation it's time to take it out for a spin ...
  78.  
  79.  
  80.  
  81.  
  82.  
  83.  
  84.  
  85.  
  86. Forging xE^ Numbers
  87.  
  88.  
  89.  
  90.  
  91.  
  92.  
  93. Now that I have established Extensible-E up to φ(ω,0,0) , let's forge a plethora of new googolism's in xE^ ...
  94.  
  95.  
  96.  
  97.  
  98. Ready for the next next level ...
  99.  
  100.  
  101.  
  102.  
  103.  
  104.  
  105.  
  106. Tethrathoth Group
  107.  
  108. (Reloaded)
  109.  
  110.  
  111.  
  112.  
  113. We can begin more or less exactly where we left off with Cascading-E Notation (E^) and Limited Extension Cascading-E Notation (LECEN), except with a greater clarity than before.
  114.  
  115.  
  116.  
  117.  
  118.  
  119. Just as before we can define:
  120.  
  121.  
  122.  
  123.  
  124.  
  125. tethrathoth = E100#^^#100
  126.  
  127.  
  128.  
  129.  
  130. The transformation laws conveniently support this definition via Law II.A under the definition of fundamental sequences. Note that Law II.A is essentially the same rule that Aarex uses at the outset of his article of Extended Cascading-E:
  131.  
  132.  
  133.  
  134.  
  135.  
  136. #^...^(#...#) = #^...(#^...^(#...))
  137.  
  138.  
  139.  
  140. ... but there are some key differences. Firstly, it only defines this sequence if the polyponent is a single hyperion. Law II.A does not apply in situations such as #^^##. Secondly, while it seems more restrictive than Aarex's rule it's actually vastly more general:
  141.  
  142.  
  143.  
  144.  
  145.  
  146.  
  147. &(α)^..k..^(#)[1] = &α
  148.  
  149.  
  150.  
  151.  
  152. &(α)^..k..^(#)[n] = &(α)^..k-1..^((α)^..k..^(#)[n-1])
  153.  
  154.  
  155.  
  156.  
  157. ... here the polybase is not restricted to just a hyperion. Rather it can be any member of the set of legal delimiters, namely the set x^. Typically this will be an epsilon number, though the rules allow the possibility of any legal delimiter being used, leading to hosts of rogues such as ##^^# for example. In this case it expands as expected...
  158.  
  159.  
  160.  
  161.  
  162. ##^^# --> ##^##^...^##^## --> ##^##^...^(##^#*##^#*...*##^#*##^#) -->
  163.  
  164.  
  165.  
  166.  
  167. ##^##^...^(##^#*##^#*...*##^#*##*##*...*##*##)
  168.  
  169.  
  170.  
  171.  
  172. This is not so strange or un-intuitive and leads to a lot of potential freedom. There is a third key difference. My rule is actually a fundamental sequence, where is Aarex's rule is not. Notice this transformation is applied regardless of what the last argument actually is. The rule is a synonym substitution, not a fundamental sequence. To give an example...
  173.  
  174.  
  175.  
  176.  
  177. @100#^^###n = @100#^#^^##n = @100#^#^#^^#n
  178.  
  179.  
  180.  
  181.  
  182. This same sequence is carried out regardless of what "n" actually is. Note that the rule doesn't terminate. It doesn't specify a base case, leading to the meaningless transformation
  183.  
  184.  
  185.  
  186.  
  187. #^^# = #^#^^
  188.  
  189.  
  190.  
  191.  
  192.  
  193. Aarex does however state a base case elsewhere as #^^# = #^#. These leads to a slightly inelegant set of synonyms...
  194.  
  195.  
  196.  
  197.  
  198.  
  199. #^^# = #^#
  200.  
  201.  
  202.  
  203.  
  204. #^^## = #^#^#
  205.  
  206.  
  207.  
  208.  
  209. #^^### = #^#^#^#
  210.  
  211.  
  212.  
  213.  
  214. In this instances we see clearly that we are dealing with synonyms here, not fundamental sequences, because this is not an equality of numeric expressions in ExE, but rather an equality of delimiters. The use of synonyms however is wasteful here as we can simply use #^^#[n] to represent the entire sequence Aarex is trying to describe! Another reason this does not seem like a good choice is that it breaks a nice symmetry we have used up to this point. Every time we are applying a fundamental sequence to a hyperion limit ordinal we can interpret it as substituting a numeric value for the keystone hyperion. For example...
  215.  
  216.  
  217.  
  218.  
  219.  
  220. #^#[n] = #^(n) = ###...## w/n #s
  221.  
  222.  
  223.  
  224.  
  225. #^##[n] = #^(#*(n)) = #^#*#^#*...*#^# w/n #^#s
  226.  
  227.  
  228.  
  229.  
  230. So note that we can interpret hyperion tetration in the following way:
  231.  
  232.  
  233.  
  234.  
  235.  
  236. #^^#[n] = #^^(n) = #^#^^(n-1) = #^#^#^^(n-2) = ... = #^#^#^...^#^# w/n #s
  237.  
  238.  
  239.  
  240.  
  241. In essence, a hyperion is just a variable container which can be replaced by any positive integer. Aarex, on the other hand, treats them as simple counters, ie:
  242.  
  243.  
  244.  
  245.  
  246.  
  247. # = 1
  248.  
  249.  
  250.  
  251.  
  252. ## = 2
  253.  
  254.  
  255.  
  256.  
  257. ### = 3
  258.  
  259.  
  260.  
  261.  
  262. etc.
  263.  
  264.  
  265.  
  266.  
  267. If that were so we'd have:
  268.  
  269.  
  270.  
  271.  
  272.  
  273. #^# = #
  274.  
  275.  
  276.  
  277.  
  278. #^## = ##
  279.  
  280.  
  281.  
  282.  
  283. #^### = ###
  284.  
  285.  
  286.  
  287.  
  288. etc.
  289.  
  290.  
  291.  
  292.  
  293. but then hyperion exponentiation would have no effect. This usage is inconsistent with the rest of Extensible-E. Although Extensible-E conventionally avoids the mixing of numbers and hyperions, the mixing has always been implied since the inception of Cascading-E. For example ...
  294.  
  295.  
  296.  
  297.  
  298. #1 = #
  299.  
  300.  
  301.  
  302.  
  303. #2 = ##
  304.  
  305.  
  306.  
  307.  
  308. #3 = ###
  309.  
  310.  
  311.  
  312.  
  313. etc.
  314.  
  315.  
  316.  
  317.  
  318. Furthermore, it was implicit in the operation of E^ that # acted as a symbol for a general number. ie #^# really means # raised to any positive integer power. With that in mind let us proceed.
  319.  
  320.  
  321.  
  322.  
  323.  
  324. Firstly let's check to make sure that our rules do properly evaluatetethrathoth:
  325.  
  326.  
  327.  
  328.  
  329.  
  330. E100#^^#100
  331.  
  332.  
  333.  
  334.  
  335. = E100#^^#[100]100
  336.  
  337.  
  338.  
  339.  
  340. = E100#^(#^^#[99])100
  341.  
  342.  
  343.  
  344.  
  345. = E100#^#^(#^^#[98])100
  346.  
  347.  
  348.  
  349.  
  350. = E100#^#^#^(#^^#[97])100
  351.  
  352.  
  353.  
  354.  
  355. ...
  356.  
  357.  
  358.  
  359.  
  360. = E100#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
  361.  
  362. #^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#
  363.  
  364. ^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
  365.  
  366. #^#^#^#^#^#^#^#^#^#^#^#^#^(#^^#[1])100
  367.  
  368.  
  369.  
  370.  
  371. = E100#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
  372.  
  373. #^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#
  374.  
  375. ^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
  376.  
  377. #^#^#^#^#^#^#^#^#^#^#^#^#^#100
  378.  
  379.  
  380.  
  381.  
  382. As you can see it behaves as expected. The #^^# delimiter is the earliest example for the application of rule II.A.
  383.  
  384.  
  385.  
  386.  
  387.  
  388. Note that Aarex defines this number as E100#^^#^#100. However according to his definitions , since #^^# = #^#, #^^## = #^#^#, #^^### = #^#^#^#, and in general #^^#n = #^^(n+1) it follows that E100#^^#^#100 = E100#^^#^#[100]100 = E100#^^#^(100)100 = E100#^^(101)100. Thus E100#^^#^#100 is actually equal to E100#^^#101 in xE^. This is actually the 101st member of the sequence {grangol,godgahlah,godgathor,godtothol,...}. I'll use a new -thol operator to allow a continuation...
  389.  
  390.  
  391.  
  392.  
  393. tethrathothitoth = E100#^^#101
  394.  
  395.  
  396.  
  397.  
  398. tethrathothi-dutoth = E100#^^#102
  399.  
  400.  
  401.  
  402.  
  403. tethrathothi-tritoth = E100#^^#103
  404.  
  405.  
  406.  
  407.  
  408. tethrathothi-tertoth = E100#^^#104
  409.  
  410.  
  411.  
  412.  
  413. ... much much much further in the sequence we have grand tethrathoth ...
  414.  
  415.  
  416.  
  417.  
  418.  
  419. E100#^^#100#2
  420.  
  421.  
  422.  
  423.  
  424. That's the tethrathoth member of the #^^#-sequence! As for evaluating it we first consider the rules and look for the earliest rule which applies: The Base Rule doesn't apply because there is more than 1 argument, The Decomposition Rule doesn't apply since '#' is not an element of x^_lim, the Terminating Rule doesn't apply because the last argument isn't 1, and the Expansion Rule doesn't apply because the last delimiter is '#'. Therefore the Recursive Rule must apply. Here I'll demonstrate the validity of the Rule:
  425.  
  426.  
  427.  
  428.  
  429. @m#n = @(@m#(n-1))
  430.  
  431.  
  432.  
  433.  
  434. Let @ = 'E100#^^#'
  435.  
  436.  
  437.  
  438.  
  439. m = 100
  440.  
  441.  
  442.  
  443.  
  444. n = 2
  445.  
  446.  
  447.  
  448.  
  449. Therefore:
  450.  
  451.  
  452.  
  453.  
  454. E100#^^#100#2 = E100#^^#(E100#^^#100#(2-1)) = E100#^^#(E100#^^#100#1)
  455.  
  456.  
  457.  
  458.  
  459. We again go through the rules again, but this time applying them to the nested expression: the Base Rule doesn't apply because there is more than 1 argument, the Decomposition Rule doesn't apply because '#' is not a member of x^_lim, the Terminating Rule does apply since the last argument = 1. Again I'll demonstrate the validity of the rule:
  460.  
  461.  
  462.  
  463.  
  464. @m&1 = @m
  465.  
  466.  
  467.  
  468.  
  469. Let @ = 'E100#^^#'
  470.  
  471.  
  472.  
  473.  
  474. m = 100
  475.  
  476.  
  477.  
  478.  
  479. Therefore:
  480.  
  481.  
  482.  
  483.  
  484. E100#^^#(E100#^^#100#1) = E100#^^#(E100#^^#100) = E100#^^#(tethrathoth)
  485.  
  486.  
  487.  
  488.  
  489. Assuming we have finished the evaluation of tethrathoth (something which is quite impossible in practice, but we can speak in hypothetical terms) the next rule to apply would be the decomposition rule since '#^^#' is a member of x^_lim. Since '#^^#' is of the general form (α)^..k..^(β) , Ruleset II applies, and since β = #, Rule II.A applies:
  490.  
  491.  
  492.  
  493.  
  494. E100#^^#(tethrathoth) = E100#^^#[tethrathoth]100
  495.  
  496.  
  497.  
  498.  
  499. = E100#^(#^^#[tethrathoth-1])100
  500.  
  501.  
  502.  
  503.  
  504. = E100#^#^(#^^#[tethrathoth-2])100
  505.  
  506.  
  507.  
  508.  
  509. = E100#^#^#^(#^^#[tethrathoth-3])100
  510.  
  511.  
  512.  
  513.  
  514. ... ... ... ... (you don't even want to know how long) ... ... ... ...
  515.  
  516.  
  517.  
  518.  
  519. = E100#^#^#^#^#^#^#^#^#^ ... ... ... ... (ditto) ... ... ... ... ^#^#^#^#^#^#^#100
  520.  
  521.  
  522.  
  523.  
  524. w/tethrathoth #s
  525.  
  526.  
  527.  
  528.  
  529. As you can see the 5 rules nicely codify xE^. In fact, these rules are the
  530.  
  531. 5 fundamental laws of Extensible-E. What this means is that these rules never change. As long as we can keep defining larger hyperion sets and define their fundamental sequences we can continue to expand Extensible-E. This also means that we won't really need to specify them over and over again from this point on and they can be taken as a given.
  532.  
  533.  
  534.  
  535.  
  536.  
  537. The ' grand ' operator should be very familiar at this point, and we can easily define grand grand tethrathoth, grand grand grand tethrathoth, etc. This is where the ' ex ' operator comes in handy. The number proceeding ' ex ' tells us how many times the following element is to be repeated. Example:
  538.  
  539.  
  540.  
  541.  
  542.  
  543. three-ex-grand tethrathoth = grand grand grand tethrathoth
  544.  
  545.  
  546.  
  547.  
  548. four-ex-grand tethrathoth = grand grand grand grand tethrathoth
  549.  
  550.  
  551.  
  552.  
  553. etc.
  554.  
  555.  
  556.  
  557.  
  558. This sequence forms the tethrathoth sequence which forms the basis of the continuation into Extended Cascading-E. We can append any number of grand's beforetethrathoth that we are capable of constructing. Using the ex-operator the following googolism's can easily be defined:
  559.  
  560.  
  561.  
  562.  
  563.  
  564. hundred-ex-grand tethrathoth = E100#^^#100#101
  565.  
  566.  
  567.  
  568.  
  569. googol-ex-grand tethrathoth = E100#^^#100#(1+E100)
  570.  
  571.  
  572.  
  573.  
  574. grangol-ex-grand tethrathoth = E100#^^#100#(1+E100#100)
  575.  
  576.  
  577.  
  578.  
  579. greagol-ex-grand tethrathoth = E100#^^#100#(1+E100#100#100)
  580.  
  581.  
  582.  
  583.  
  584. gigangol-ex-grand tethrathoth = E100#^^#100#(1+E100#100#100#100)
  585.  
  586.  
  587.  
  588.  
  589. gugold-ex-grand tethrathoth = E100#^^#100#(1+E100##100)
  590.  
  591.  
  592.  
  593.  
  594. godgahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#100)
  595.  
  596.  
  597.  
  598.  
  599. tethrathoth-ex-grand tethrathoth = E100#^^#100#(1+E100#^#100)
  600.  
  601.  
  602.  
  603.  
  604. tethrathoth-ex-grand tethrathoth-ex-grand tethrathoth
  605.  
  606.  
  607.  
  608.  
  609. = E100#^^#100#(1+E100#^^#100#(1+E100#^#100))
  610.  
  611.  
  612.  
  613.  
  614. This is of coarse just a primitive recursive extension so let's move on. We can notate the nth member of the tethrathoth sequence as E100#^^#100#n. The 100th member of the tethrathoth sequence would be E100#^^#100#100. Notice that if we let @ = 'E100#^^#' , we can write @100#100. This looks similar to grangol (E100#100). From this I coined the name grantethrathoth from grangol + tethrathoth. The problem is that generalizing this leads to potential problems. To allow for greater and easier generalization I will introduce the carta-operator (from the greek root carta, meaning map). Let G and H be googolism's in ExE. Let H be represented by @100. Let G be represented as E%. Then define G-carta-H as @%. Here G is being mapped to H. That is, we can imagine H as the 100th member of some sequence. We can map googol to this by treating it as the 100th member of the sequence 10,100,1000,10000,...etc. This analogy allows us to map any of the googolism's to our new sequence H. Think of @n as a function. @100#100 means grangol mapped to the function @n. This makes completely routine many of the previous googolism's mentioned in the Cascading-E article. Here are some examples:
  615.  
  616.  
  617.  
  618.  
  619.  
  620. grangol-carta-tethrathoth = grantethrathoth = E100#^^#100#100
  621.  
  622.  
  623.  
  624.  
  625. greagol-carta-tethrathoth = greatethrathoth = E100#^^#100#100#100
  626.  
  627.  
  628.  
  629.  
  630. gigangol-carta-tethrathoth = gigantethrathoth = E100#^^#100#100#100#100
  631.  
  632.  
  633.  
  634.  
  635. gorgegol-carta-tethrathoth = gorgetethrathoth = E100#^^#100##5
  636.  
  637.  
  638.  
  639.  
  640. gulgol-carta-tethrathoth = gultethrathoth = E100#^^#100##6
  641.  
  642.  
  643.  
  644.  
  645. gaspgol-carta-tethrathoth = gasptethrathoth = E100#^^#100##7
  646.  
  647.  
  648.  
  649.  
  650. ginorgol-carta-tethrathoth = ginortethrathoth = E100#^^#100##8
  651.  
  652.  
  653.  
  654.  
  655. This is the point at which I stopped in the previous article. The main reason was that the above pattern does not make it readily apparent how gugold and those after it should be appended to tethrathoth. Aarex took this opportunity to attempt to continue the pattern. I'll offer my own continuation below:
  656.  
  657.  
  658.  
  659.  
  660.  
  661. gugolda-carta-tethrathoth = E100#^^#100##100
  662.  
  663.  
  664.  
  665.  
  666. graatagolda-carta-tethrathoth = E100#^^#100##100#100
  667.  
  668.  
  669.  
  670.  
  671. greegolda-carta-tethrathoth = E100#^^#100##100#100#100
  672.  
  673.  
  674.  
  675.  
  676. grinningolda-carta-tethrathoth = E100#^^#100##100#100#100#100
  677.  
  678.  
  679.  
  680.  
  681. gugolthra-carta-tethrathoth = E100#^^#100##100##100
  682.  
  683.  
  684.  
  685.  
  686. gugoltesla-carta-tethrathoth = E100#^^#100##100##100##100
  687.  
  688.  
  689.  
  690.  
  691. throogola-carta-tethrathoth = E100#^^#100###100
  692.  
  693.  
  694.  
  695.  
  696. tristo-throogola-carta-tethrathoth = E100#^^#100###100###100
  697.  
  698.  
  699.  
  700.  
  701. teroogola-carta-tethrathoth = E100#^^#100####100
  702.  
  703.  
  704.  
  705.  
  706. ...
  707.  
  708.  
  709.  
  710.  
  711. godgahlah-carta-tethrathoth = E100#^^#100#^#100
  712.  
  713.  
  714.  
  715.  
  716. grand godgahlah-carta-tethrathoth = E100#^^#100#^#100#2
  717.  
  718.  
  719.  
  720.  
  721. grangahlah-carta-tethrathoth = E100#^^#100#^#100#100
  722.  
  723.  
  724.  
  725.  
  726. greagahlah-carta-tethrathoth = E100#^^#100#^#100#100#100
  727.  
  728.  
  729.  
  730.  
  731. gigangahlah-carta-tethrathoth = E100#^^#100#^#100#100#100#100
  732.  
  733.  
  734.  
  735.  
  736. gorgegahlah-carta-tethrathoth = E100#^^#100#^#100##5
  737.  
  738.  
  739.  
  740.  
  741. gulgahlah-carta-tethrathoth = E100#^^#100#^#100##6
  742.  
  743.  
  744.  
  745.  
  746. gaspgahlah-carta-tethrathoth = E100#^^#100#^#100##7
  747.  
  748.  
  749.  
  750.  
  751. ginorgahlah-carta-tethrathoth = E100#^^#100#^#100##8
  752.  
  753.  
  754.  
  755.  
  756. gugoldgahlah-carta-tethrathoth = E100#^^#100#^#100##100
  757.  
  758.  
  759.  
  760.  
  761. gugolthragahlah-carta-tethrathoth = E100#^^#100#^#100##100##100
  762.  
  763.  
  764.  
  765.  
  766. gugolteslagahlah-carta-tethrathoth = E100#^^#100#^#100##100##100##100
  767.  
  768.  
  769.  
  770.  
  771. throogahlah-carta-tethrathoth = E100#^^#100#^#100###100
  772.  
  773.  
  774.  
  775.  
  776. teroogahlah-carta-tethrathoth = E100#^^#100#^#100####100
  777.  
  778.  
  779.  
  780.  
  781. gotrigahlah-carta-tethrathoth = E100#^^#100#^#100#^#100
  782.  
  783.  
  784.  
  785.  
  786. gotergahlah-carta-tethrathoth = E100#^^#100#^#100#^#100#^#100
  787.  
  788.  
  789.  
  790.  
  791. ...
  792.  
  793.  
  794.  
  795.  
  796. godgoldgahlah-carta-tethrathoth = E100#^^#100#^#*#100
  797.  
  798.  
  799.  
  800.  
  801.  
  802. godthroogahlah-carta-tethrathoth = E100#^^#100#^#*##100
  803.  
  804.  
  805.  
  806.  
  807. godteroogahlah-carta-tethrathoth = E100#^^#100#^#*###100
  808.  
  809.  
  810.  
  811.  
  812. ...
  813.  
  814.  
  815.  
  816.  
  817. deutero-godgahlah-carta-tethrathoth = E100#^^#100#^#*#^#100
  818.  
  819.  
  820.  
  821.  
  822. trito-godgahlah-carta-tethrathoth E100#^^#100#^#*#^#*#^#100
  823.  
  824.  
  825.  
  826.  
  827. teterto-godgahlah-carta-tethrathoth = E100#^^#100#^#*#^#*#^#*#^#100
  828.  
  829.  
  830.  
  831.  
  832. ...
  833.  
  834.  
  835.  
  836.  
  837. gridgahlah-carta-tethrathoth = E100#^^#100#^##100
  838.  
  839.  
  840.  
  841.  
  842. kubikahlah-carta-tethrathoth = E100#^^#100#^###100
  843.  
  844.  
  845.  
  846.  
  847. quarticahlah-carta-tethrathoth = E100#^^#100#^####100
  848.  
  849.  
  850.  
  851.  
  852. ...
  853.  
  854.  
  855.  
  856.  
  857. godgathor-carta-tethrathoth = E100#^^#100#^#^#100
  858.  
  859.  
  860.  
  861.  
  862. gralgathor-carta-tethrathoth = E100#^^#100#^#^##100
  863.  
  864.  
  865.  
  866.  
  867. godtothol-carta-tethrathoth = E100#^^#100#^#^#^#100
  868.  
  869.  
  870.  
  871.  
  872. ...
  873.  
  874.  
  875.  
  876.  
  877. ... this brings us to tethrathoth-carta-tethrathoth , E100#^^#100#^^#100, also called tethratrithoth. This leads to an even faster diagonalization...
  878.  
  879.  
  880.  
  881.  
  882.  
  883. tethratrithoth = E100#^^#100#^^#100
  884.  
  885.  
  886.  
  887.  
  888. tethraterthoth = E100#^^#100#^^#100#^^#100
  889.  
  890.  
  891.  
  892.  
  893.  
  894. tethrapethoth = E100#^^#*#5
  895.  
  896.  
  897.  
  898.  
  899. tethra-exthoth = E100#^^#*#6
  900.  
  901.  
  902.  
  903.  
  904. tethra-epthoth = E100#^^#*#7
  905.  
  906.  
  907.  
  908.  
  909. tethra-octhoth = E100#^^#*#8
  910.  
  911.  
  912.  
  913.  
  914. ...
  915.  
  916.  
  917.  
  918.  
  919. This leads to another level of diagonalization even more ridiculous...
  920.  
  921.  
  922.  
  923.  
  924.  
  925. E100#^^#*#100
  926.  
  927.  
  928.  
  929.  
  930. E100#^^#*##100
  931.  
  932.  
  933.  
  934.  
  935. E100#^^#*#^#100
  936.  
  937.  
  938.  
  939.  
  940. E100#^^#*#^#*#100
  941.  
  942.  
  943.  
  944.  
  945. E100#^^#*#^#*#^#100
  946.  
  947.  
  948.  
  949.  
  950. E100#^^#*#^##100
  951.  
  952.  
  953.  
  954.  
  955. E100#^^#*#^#^#100
  956.  
  957.  
  958.  
  959.  
  960. E100#^^#*#^#^#^#100
  961.  
  962.  
  963.  
  964.  
  965. ...
  966.  
  967.  
  968.  
  969.  
  970. This eventually leads to E100#^^#*#^^#100. Here we have the hyperion-power operators, deutero, trito, teterto, etc. These take any hyper-factor, &, and the replace it with &^(n). Where deutero = 2 , trito = 3, teterto = 4, etc.
  971.  
  972. Thus we have:
  973.  
  974.  
  975.  
  976.  
  977.  
  978. deutero-tethrathoth = E100#^^#*#^^#100 = E100(#^^#)^#2
  979.  
  980.  
  981.  
  982.  
  983. trito-tethrathoth = E100#^^#*#^^#*#^^#100 = E100(#^^#)^#3
  984.  
  985.  
  986.  
  987.  
  988. teterto-tethrathoth = E100#^^#*#^^#*#^^#*#^^#100 = E100(#^^#)^#4
  989.  
  990.  
  991.  
  992.  
  993. ...
  994.  
  995.  
  996.  
  997.  
  998. hecato-tethrathoth = E100(#^^#)^#100
  999.  
  1000.  
  1001.  
  1002.  
  1003. Aarex dubs the hecato-tethrathoth the 'tethrathor'. His definition however differs significantly, so let's examine it:
  1004.  
  1005.  
  1006.  
  1007.  
  1008.  
  1009. 'tethrathor' = E100#^(#^^(#^#/#)*#)100
  1010.  
  1011.  
  1012.  
  1013.  
  1014. The idea here is actually quite interesting. He uses the /# to avoid the problem that occurs in the ordinal ω^(ε0+1) of offset (see article 4.2.5). We can define /# as hyperion division, something I already suggested in the previous article as a way to define E^. Here is how this would be evaluated...
  1015.  
  1016.  
  1017.  
  1018.  
  1019. E100#^(#^^(#^#/#)*#)100 = E100(#^(#^^(#^#/#))^(100)100 =
  1020.  
  1021.  
  1022.  
  1023.  
  1024. E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^#/#)100
  1025.  
  1026.  
  1027.  
  1028.  
  1029. = E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^(100)/#)100
  1030.  
  1031.  
  1032.  
  1033.  
  1034. = E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^99))100
  1035.  
  1036.  
  1037.  
  1038.  
  1039. = E100(#^(#^^(#^#/#))^(99)*#^(#^^100)100
  1040.  
  1041.  
  1042.  
  1043.  
  1044. = E100(#^(#^^(#^#/#))^(99)*#^^(101)100
  1045.  
  1046.  
  1047.  
  1048.  
  1049. As you can see there is still an offset created by this system. However, to be fair, things are functional up to this point. Interestingly enough, xE^ also can support this format, even though the rules were not designed to. It's part of the rogue set of delimiters. For example:
  1050.  
  1051.  
  1052.  
  1053.  
  1054.  
  1055. E100#^(#^^#*#)100
  1056.  
  1057.  
  1058.  
  1059.  
  1060. By Rule I.B we have that # is being raised to a successor. So following the rule we get...
  1061.  
  1062.  
  1063.  
  1064.  
  1065.  
  1066. E100#^(#^^#*#)100 = E100(#^(#^^#))^(100)100 =
  1067.  
  1068.  
  1069.  
  1070.  
  1071. E100(#^(#^^#))^(99)*#^#^^#100
  1072.  
  1073.  
  1074.  
  1075.  
  1076. = E100(#^(#^^#))^(99)*#^#^^(100)100
  1077.  
  1078.  
  1079.  
  1080.  
  1081. = E100(#^(#^^#))^(99)*#^^(101)100
  1082.  
  1083.  
  1084.  
  1085.  
  1086. Although the rules allow for the cantor normal forms, it has the same problem as well ... it has a slight offset. This is part of why I have opted for the more natural extension of stacking epsilon numbers. I should also note that E100(#^^(101))^#100 is not the same thing as E100#^(#^^#*#)100 even if they seem like they should be the same. The reason for this is that #^^(101) is a E^ delimiter, where as #^^# is a xE^ delimiter. They behave very differently, and #^^# has a much faster growing fundamental sequence, although it takes a while to catch up. Remember that in the case of E100#^(#^^#*#)100, we are actually getting 100 iterations of #^(#^^#) not #^(#^^100). Rather, only the last one becomes #^(#^^100). It's a long time before the 2nd to last gets it's turn. By the time it does the final argument has become mind-bogglingly massive, call it X. The 2nd to last then becomes #^(#^^X) = #^^(X+1). The +1 is an additional offset. Each #^(#^^#) will add 1 to the height of the hyperion power tower. Mind you, the effect is negligible, but it does guarantee that E100(#^^#)^#100 < E100#^(#^^#*#)100 , even though ordinal arithmetic would tell us these ordinals, (#^^#)^# and #^(#^^#*#), are the same. In any case I'll appropriate this interesting case and say:
  1087.  
  1088.  
  1089.  
  1090.  
  1091. tethrathor = E100#^(#^^#*#)100
  1092.  
  1093.  
  1094.  
  1095.  
  1096. There is a way to correct this problem. Define #-1 such that #-1[n] = #[n]-1. Treating # as a indefinite value, rather than as ω, allows for much more flexibility. We can then actually define...
  1097.  
  1098.  
  1099.  
  1100.  
  1101. hecato-tethrathoth = E100#^(#^^(#-1)*#)100
  1102.  
  1103.  
  1104.  
  1105.  
  1106. This was the meaning Aarex was going for. I should note that this is an illegal delimiter not strictly supported by the rules of xE^. However it isn't difficult to tweak them a bit to allow such forms. Here is how this would be evaluated...
  1107.  
  1108.  
  1109.  
  1110.  
  1111.  
  1112. E100#^(#^^(#-1)*#)100 =
  1113.  
  1114.  
  1115.  
  1116.  
  1117. E100(#^(#^^(#-1)))^(100)100
  1118.  
  1119.  
  1120.  
  1121.  
  1122. = E100(#^(#^^(#-1))^(99)*#^(#^^(#-1))100
  1123.  
  1124.  
  1125.  
  1126.  
  1127. = E100(#^(#^^(#-1))^(99)*#^(#^^(100-1))100
  1128.  
  1129.  
  1130.  
  1131.  
  1132. = E100(#^(#^^(#-1))^(99)*#^(#^^(99))100
  1133.  
  1134.  
  1135.  
  1136.  
  1137. = E100(#^(#^^(#-1))^(99)*#^^(100)100
  1138.  
  1139.  
  1140.  
  1141.  
  1142. This little correction factor will propagate throughout the expression and evaluation process.
  1143.  
  1144.  
  1145.  
  1146.  
  1147.  
  1148. Although this is the standard progression used past ε(0) in the fast growing hierarchy, I find the offset to be somewhat unnatural. This is why I have opted instead for the stacking sequence, that treats ε(0) as a new base on which to stack ordinal exponents. The two forms leads to slightly different functions unless a correction factor is implemented as above.
  1149.  
  1150.  
  1151. Aarex's terms from the 'tethrathor' group to the 'todatriath' group lie below ε(1). I did not coin any googolism's in the range between hecato-tethrathoth, and Monster-Giant. Here I'll provide some terms:
  1152.  
  1153.  
  1154. tethrafact = E100(#^^#)^#100
  1155.  
  1156.  
  1157.  
  1158.  
  1159. (from tetration + factor because #^^# is the only factor of the hyper-product)
  1160.  
  1161. griduutethrathoth = E100(#^^#)^##100
  1162.  
  1163. kubicutethrathoth = E100(#^^#)^###100
  1164.  
  1165.  
  1166.  
  1167. quarticutethrathoth = E100(#^^#)^####100
  1168.  
  1169.  
  1170.  
  1171. quinticutethrathoth = E100(#^^#)^#^#5
  1172.  
  1173.  
  1174.  
  1175. sexticutethrathoth = E100(#^^#)^#^#6
  1176.  
  1177.  
  1178.  
  1179. septicutethrathoth = E100(#^^#)^#^#7
  1180.  
  1181.  
  1182.  
  1183. octicutethrathoth = E100(#^^#)^#^#8
  1184.  
  1185.  
  1186.  
  1187. nonicutethrathoth = E100(#^^#)^#^#9
  1188.  
  1189.  
  1190.  
  1191. decicutethrathoth = E100(#^^#)^#^#10
  1192.  
  1193. ...
  1194.  
  1195.  
  1196.  
  1197. centicutethrathoth = E100(#^^#)^#^#100
  1198.  
  1199.  
  1200. ... but this isn't nearly extensible enough, and we want more ... many many more intermediate terms before we get up to Monster-Giant. See if you can figure out these constructions ...
  1201.  
  1202.  
  1203. tethragodgathor = E100(#^^#)^#^#100
  1204.  
  1205.  
  1206.  
  1207. tethragralgathor = E100(#^^#)^#^##100
  1208.  
  1209.  
  1210.  
  1211. tethrathraelgathor = E100(#^^#)^#^###100
  1212.  
  1213.  
  1214.  
  1215. tethraterinngathor = E100(#^^#)^#^####100
  1216.  
  1217.  
  1218.  
  1219. tethrapehaelgathor = E100(#^^#)^#^#^#5
  1220.  
  1221.  
  1222.  
  1223. tethrahexaelgathor = E100(#^^#)^#^#^#6
  1224.  
  1225.  
  1226.  
  1227. tethraheptaelgathor = E100(#^^#)^#^#^#7
  1228.  
  1229.  
  1230.  
  1231. tethra-octaelgathor = E100(#^^#)^#^#^#8
  1232.  
  1233. ...
  1234.  
  1235.  
  1236.  
  1237.  
  1238. tethragodtothol = E100(#^^#)^#^#^#100
  1239.  
  1240.  
  1241.  
  1242. tethragraltothol = E100(#^^#)^#^#^##100
  1243.  
  1244.  
  1245.  
  1246. tethrathraeltothol = E100(#^^#)^#^#^###100
  1247.  
  1248.  
  1249.  
  1250. tethraterinntothol = E100(#^^#)^#^#^####100
  1251.  
  1252.  
  1253.  
  1254. tethrapehaeltothol = E100(#^^#)^#^#^#^#5
  1255.  
  1256.  
  1257.  
  1258. tethrahexaeltothol = E100(#^^#)^#^#^#^#6
  1259.  
  1260.  
  1261.  
  1262. tethraheptaeltothol = E100(#^^#)^#^#^#^#7
  1263.  
  1264.  
  1265.  
  1266. tethra-octaeltothol = E100(#^^#)^#^#^#^#8
  1267.  
  1268. ...
  1269.  
  1270.  
  1271.  
  1272. tethragodtertathol = E100(#^^#)^#^#^#^#100
  1273.  
  1274.  
  1275.  
  1276. tethragodpeptathol = E100(#^^#)^(#^^#)5
  1277.  
  1278.  
  1279.  
  1280. tethragodextathol = E100(#^^#)^(#^^#)6
  1281.  
  1282.  
  1283.  
  1284. tethragodeptathol = E100(#^^#)^(#^^#)7
  1285.  
  1286.  
  1287.  
  1288. tethragodoctathol = E100(#^^#)^(#^^#)8
  1289.  
  1290. ...
  1291.  
  1292.  
  1293.  
  1294. tethra-tethrathoth = E100(#^^#)^(#^^#)100
  1295.  
  1296.  
  1297.  
  1298. Now to get even further along in the progression...
  1299.  
  1300.  
  1301. tethraduliath = E100(#^^#)^(#^^#)100
  1302.  
  1303.  
  1304.  
  1305.  
  1306. (also tethrathoth-doppelex)
  1307.  
  1308.  
  1309.  
  1310. tethradulifact = E100(#^^#)^(#^^#*#)100
  1311.  
  1312.  
  1313.  
  1314. griduutethraduliath = E100(#^^#)^(#^^#*##)100
  1315.  
  1316.  
  1317.  
  1318. kubicutethraduliath = E100(#^^#)^(#^^#*###)100
  1319.  
  1320.  
  1321.  
  1322. quarticutethraduliath = E100(#^^#)^(#^^#*####)100
  1323.  
  1324.  
  1325.  
  1326. quinticutethraduliath = E100(#^^#)^(#^^#*#^#)5
  1327.  
  1328.  
  1329.  
  1330. sexticutethraduliath = E100(#^^#)^(#^^#*#^#)6
  1331.  
  1332.  
  1333.  
  1334. septicutethraduliath = E100(#^^#)^(#^^#*#^#)7
  1335.  
  1336.  
  1337.  
  1338. octicutethraduliath = E100(#^^#)^(#^^#*#^#)8
  1339.  
  1340.  
  1341.  
  1342.  
  1343. nonicutethraduliath = E100(#^^#)^(#^^#*#^#)9
  1344.  
  1345.  
  1346.  
  1347.  
  1348. decicutethraduliath = E100(#^^#)^(#^^#*#^#)10
  1349.  
  1350. ...
  1351.  
  1352.  
  1353.  
  1354. tethraduli-godgathor = E100(#^^#)^(#^^#*#^#)100
  1355.  
  1356.  
  1357.  
  1358. tethraduli-gralgathor = E100(#^^#)^(#^^#*#^##)100
  1359.  
  1360.  
  1361.  
  1362. tethraduli-thraelgathor = E100(#^^#)^(#^^#*#^###)100
  1363.  
  1364.  
  1365.  
  1366. tethraduli-terinngathor = E100(#^^#)^(#^^#*#^####)100
  1367.  
  1368. ...
  1369.  
  1370.  
  1371.  
  1372. tethraduli-godtothol = E100(#^^#)^(#^^#*#^#^#)100
  1373.  
  1374.  
  1375.  
  1376. tethraduli-godtertathol = E100(#^^#)^(#^^#*#^#^#^#)100
  1377.  
  1378.  
  1379.  
  1380. tethraduli-godpeptathol = E100(#^^#)^(#^^#*#^^#)5
  1381.  
  1382.  
  1383.  
  1384. tethraduli-godextathol = E100(#^^#)^(#^^#*#^^#)6
  1385.  
  1386.  
  1387.  
  1388. tethraduli-godeptathol = E100(#^^#)^(#^^#*#^^#)7
  1389.  
  1390.  
  1391.  
  1392. tethraduli-godoctathol = E100(#^^#)^(#^^#*#^^#)8
  1393.  
  1394. ...
  1395.  
  1396.  
  1397.  
  1398.  
  1399. tethrathruliath = E100(#^^#)^(#^^#*#^^#)100
  1400.  
  1401.  
  1402.  
  1403. tethrathrulifact = E100(#^^#)^(#^^#*#^^#*#)100
  1404.  
  1405.  
  1406.  
  1407. griduutethrathruliath = E100(#^^#)^(#^^#*#^^#*##)100
  1408.  
  1409.  
  1410.  
  1411. cubicutethrathruliath = E100(#^^#)^(#^^#*#^^#*###)100
  1412.  
  1413.  
  1414.  
  1415. tethrathruliquarticulus = E100(#^^#)^(#^^#*#^^#*####)100
  1416.  
  1417.  
  1418.  
  1419. tethrathruliquinticulus = E100(#^^#)^(#^^#*#^^#*#^#)5
  1420.  
  1421.  
  1422.  
  1423. tethrathrulisexticulus = E100(#^^#)^(#^^#*#^^#*#^#)6
  1424.  
  1425.  
  1426.  
  1427. tethrathrulisepticulus = E100(#^^#)^(#^^#*#^^#*#^#)7
  1428.  
  1429.  
  1430.  
  1431. tethrathruliocticulus = E100(#^^#)^(#^^#*#^^#*#^#)8
  1432.  
  1433. ...
  1434.  
  1435.  
  1436.  
  1437. tethrathruli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#)2
  1438.  
  1439.  
  1440.  
  1441. tethrathruli-godtothol = E100(#^^#)^(#^^#*#^^#*#^^#)3
  1442.  
  1443.  
  1444.  
  1445. tethrathruli-godtertathol = E100(#^^#)^(#^^#*#^^#*#^^#)4
  1446.  
  1447.  
  1448.  
  1449. tethrathruli-godpeptathol = E100(#^^#)^(#^^#*#^^#*#^^#)5
  1450.  
  1451.  
  1452.  
  1453. tethrathruli-godextathol = E100(#^^#)^(#^^#*#^^#*#^^#)6
  1454.  
  1455.  
  1456.  
  1457. tethrathruli-godeptathol = E100(#^^#)^(#^^#*#^^#*#^^#)7
  1458.  
  1459.  
  1460.  
  1461. tethrathruli-godoctathol = E100(#^^#)^(#^^#*#^^#*#^^#)8
  1462.  
  1463. ...
  1464.  
  1465.  
  1466.  
  1467. tethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#)100
  1468.  
  1469.  
  1470.  
  1471. tethraterlichain = E100(#^^#)^(#^^#*#^^#*#^^#*#)100
  1472.  
  1473.  
  1474.  
  1475. tethraterligridulus = E100(#^^#)^(#^^#*#^^#*#^^#*##)100
  1476.  
  1477. tethraterlicubiculus = E100(#^^#)^(#^^#*#^^#*#^^#*###)100
  1478.  
  1479. tethraterliquarticulus = E100(#^^#)^(#^^#*#^^#*#^^#*####)100
  1480.  
  1481. tethraterliquinticulus = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)5
  1482.  
  1483. tethraterlisexticulus = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)6
  1484.  
  1485. tethraterlisepticulus = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)7
  1486.  
  1487. tethraterliocticulus = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)8
  1488.  
  1489.  
  1490.  
  1491.  
  1492. ...
  1493.  
  1494.  
  1495.  
  1496. tethraterli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#)2
  1497.  
  1498. ...
  1499.  
  1500.  
  1501.  
  1502. tethrapepliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#)100
  1503.  
  1504.  
  1505.  
  1506. tethrapeplichain = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#)100
  1507.  
  1508. ...
  1509.  
  1510.  
  1511.  
  1512. tethrapepli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#)2
  1513.  
  1514. ...
  1515.  
  1516.  
  1517.  
  1518. tethra-exliath = E100(#^^#)^(#^^#)^#5
  1519.  
  1520.  
  1521.  
  1522. tethra-epliath = E100(#^^#)^(#^^#)^#6
  1523.  
  1524.  
  1525.  
  1526. tethra-ocliath = E100(#^^#)^(#^^#)^#7
  1527.  
  1528. ...
  1529.  
  1530.  
  1531.  
  1532. Monster-Giant = E100(#^^#)^(#^^#)^#100 =
  1533.  
  1534.  
  1535.  
  1536. E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1537. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1538. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1539. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1540. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1541. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1542. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1543. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
  1544. #^^#*#^^#*#^^#*#^^#*#^^#*#^^#)100
  1545.  
  1546.  
  1547.  
  1548. What could be better than that? ...
  1549.  
  1550.  
  1551.  
  1552. grand Monster-Giant = E100(#^^#)^(#^^#)^#100#2 =
  1553.  
  1554.  
  1555.  
  1556. E100(#^^#)^(#^^#)^#[Monster-Giant]100 =
  1557.  
  1558.  
  1559.  
  1560. E100(#^^#)^(#^^#*#^^#*#^^#*#^^#* ... ... ... ... #^^#*#^^#*#^^#*#^^#)100
  1561.  
  1562.  
  1563.  
  1564. w/Monster-Giant #^^#s in the exponent
  1565.  
  1566.  
  1567.  
  1568. What's even better than that?! ...
  1569.  
  1570.  
  1571.  
  1572. Monster-Gigantri = E100(#^^#)^(#^^#)^#100(#^^#)^(#^^#)^#100
  1573.  
  1574. Monster-Gigantet = E100(#^^#)^(#^^#)^#*#4
  1575.  
  1576. Monster-Giganpent = E100(#^^#)^(#^^#)^#*#5
  1577.  
  1578. Monster-Gigantex = E100(#^^#)^(#^^#)^#*#6
  1579.  
  1580. Monster-Gigantep = E100(#^^#)^(#^^#)^#*#7
  1581.  
  1582. Monster-Gigantoch = E100(#^^#)^(#^^#)^#*#8
  1583.  
  1584.  
  1585.  
  1586. what's even better than that?!? ...
  1587.  
  1588.  
  1589.  
  1590. deutero-Monster-Giant = E100(#^^#)^(#^^#)^#*(#^^#)^(#^^#)^#100
  1591.  
  1592.  
  1593.  
  1594. trito-Monster-Giant = E100(#^^#)^((#^^#)^#*#)3
  1595.  
  1596.  
  1597. teterto-Monster-Giant = E100(#^^#)^((#^^#)^#*#)4
  1598.  
  1599. ...
  1600.  
  1601.  
  1602.  
  1603. hecato-Monster-Giant = E100(#^^#)^((#^^#)^#*#)100
  1604.  
  1605.  
  1606.  
  1607.  
  1608.  
  1609. Here things get kinda complicated ...
  1610.  
  1611.  
  1612.  
  1613.  
  1614.  
  1615. E100(#^^#)^((#^^#)^#*#^^#)100
  1616.  
  1617.  
  1618.  
  1619. Note that this number IS NOT E100(#^^#)^(#^^#)^#101. This number is much much smaller than E100(#^^#)^((#^^#)^#*#^^#)100. Remember that only the last #^^# get's decomposed. Only once this completely decays do we get to decompose (#^^#)^#. At this point however "n", the last argument, is so unfathomably large, that comparison with the Monster-Giant is absurdly insulting... and we are just getting started with xE^ ...
  1620.  
  1621.  
  1622.  
  1623. tethra-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#)100
  1624.  
  1625.  
  1626.  
  1627. tethraduli-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#*#^^#)100
  1628.  
  1629.  
  1630.  
  1631. tethrathruli-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#*#^^#*#^^#)100
  1632.  
  1633.  
  1634.  
  1635. tethraterli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)4
  1636.  
  1637.  
  1638.  
  1639. tethrapepli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)5
  1640.  
  1641. tethraexli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)6
  1642.  
  1643. tethraepli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)7
  1644.  
  1645. tethraocli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)8
  1646.  
  1647.  
  1648.  
  1649. Monster Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)100
  1650.  
  1651.  
  1652.  
  1653. alternatively ...
  1654.  
  1655.  
  1656.  
  1657. two-ex-Monster-Giant = E100(#^^#)^(#^^#)^##2
  1658.  
  1659.  
  1660.  
  1661. three-ex-Monster-Giant = E100(#^^#)^(#^^#)^##3
  1662.  
  1663.  
  1664.  
  1665. ...
  1666.  
  1667.  
  1668.  
  1669. hundred-ex-Monster-Giant = E100(#^^#)^(#^^#)^##100
  1670.  
  1671.  
  1672.  
  1673. Monster-Giant-ex-Monster-Giant = E100(#^^#)^(#^^#)^##[Monster-Giant]100
  1674.  
  1675.  
  1676.  
  1677.  
  1678.  
  1679. grand hundred-ex-Monster-Giant = E100(#^^#)^(#^^#)^##100#2 =
  1680.  
  1681.  
  1682.  
  1683. E100(#^^#)^(#^^#)^##[hundred-ex-Monster-Giant]100
  1684.  
  1685.  
  1686. With that exhausted we need something new ...
  1687.  
  1688.  
  1689.  
  1690. Monster-Grid = E100(#^^#)^(#^^#)^##100
  1691.  
  1692.  
  1693.  
  1694. Monster-Cube = E100(#^^#)^(#^^#)^###100
  1695.  
  1696.  
  1697.  
  1698. Monster-Tesseract = E100(#^^#)^(#^^#)^####100
  1699.  
  1700.  
  1701.  
  1702. ...
  1703.  
  1704.  
  1705.  
  1706. Monster-Hecateract = E100(#^^#)^(#^^#)^#^#100 =
  1707.  
  1708.  
  1709.  
  1710. E100(#^^#)^(#^^#)^###########################################
  1711.  
  1712. #########################################################100
  1713.  
  1714.  
  1715.  
  1716. Diagonalizing on a larger scale we can say...
  1717.  
  1718.  
  1719.  
  1720. Super Monster-Giant = E100(#^^#)^(#^^#)^(#^^#)^#100
  1721.  
  1722.  
  1723.  
  1724. Super Monster-Grid = E100(#^^#)^(#^^#)^(#^^#)^##100
  1725.  
  1726.  
  1727.  
  1728. Super Monster-Cube = E100(#^^#)^(#^^#)^(#^^#)^###100
  1729.  
  1730.  
  1731.  
  1732. Super Monster-Tesseract = E100(#^^#)^(#^^#)^(#^^#)^####100
  1733.  
  1734.  
  1735.  
  1736. ...
  1737.  
  1738.  
  1739.  
  1740. Super Monster-Hecateract = E100(#^^#)^(#^^#)^(#^^#)^#^#100
  1741.  
  1742.  
  1743.  
  1744. ...
  1745.  
  1746.  
  1747.  
  1748. Double-Super Monster-Giant = E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100
  1749.  
  1750.  
  1751.  
  1752. Triple-Super Monster-Giant = E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100
  1753.  
  1754.  
  1755.  
  1756. ...
  1757.  
  1758.  
  1759.  
  1760. Here is another diagonalization series that goes even further...
  1761.  
  1762.  
  1763.  
  1764. tethrathoth-doppelux = E100(#^^#)^(#^^#)100
  1765.  
  1766.  
  1767.  
  1768. tethrathoth-treppelux = E100(#^^#)^(#^^#)^(#^^#)100
  1769.  
  1770.  
  1771.  
  1772. tethrathoth-quadrupelux = E100(#^^#)^(#^^#)^(#^^#)^(#^^#)100
  1773.  
  1774.  
  1775.  
  1776. tethrathoth-quintupelux = E100(#^^#)^^#5
  1777.  
  1778.  
  1779.  
  1780. tethrathoth-sextupelux = E100(#^^#)^^#6
  1781.  
  1782.  
  1783.  
  1784. tethrathoth-septupelux = E100(#^^#)^^#7
  1785.  
  1786.  
  1787.  
  1788. tethrathoth-octupelux = E100(#^^#)^^#8
  1789.  
  1790.  
  1791.  
  1792. ...
  1793.  
  1794.  
  1795.  
  1796. terrible tethrathoth = E100(#^^#)^^#100 =
  1797.  
  1798.  
  1799.  
  1800. E100(#^^#)^(#^^#)^(#^^#)^ ... ... ^(#^^#)^(#^^#)^(#^^#)100 w/100 #^^#s
  1801.  
  1802.  
  1803.  
  1804. terrible tethrathoth-doppelux = E100((#^^#)^^#)^((#^^#)^^#)100
  1805.  
  1806.  
  1807.  
  1808. terrible tethrathoth-treppelux = E100((#^^#)^^#)^((#^^#)^^#)^((#^^#)^^#)100
  1809.  
  1810.  
  1811.  
  1812. terrible tethrathoth-quadrupelux = E100((#^^#)^^#)^^#4
  1813.  
  1814.  
  1815.  
  1816. terrible tethrathoth-quintupelux = E100((#^^#)^^#)^^#5
  1817.  
  1818.  
  1819.  
  1820. terrible tethrathoth-sextupelux = E100((#^^#)^^#)^^#6
  1821.  
  1822.  
  1823.  
  1824. terrible tethrathoth-septupelux = E100((#^^#)^^#)^^#7
  1825.  
  1826.  
  1827.  
  1828. terrible tethrathoth-octupelux = E100((#^^#)^^#)^^#8
  1829.  
  1830.  
  1831.  
  1832. ...
  1833.  
  1834.  
  1835.  
  1836. double-terrible tethrathoth = E100((#^^#)^^#)^^#100
  1837.  
  1838.  
  1839.  
  1840. double-terrible tethrathoth-doppelux = E100(((#^^#)^^#)^^#)^(((#^^#)^^#)^^#)100
  1841.  
  1842.  
  1843.  
  1844. double-terrible tethrathoth-treppelux = E100(((#^^#)^^#)^^#)^^#3
  1845.  
  1846.  
  1847.  
  1848. double-terrible tethrathoth-quadrupelux = E100(((#^^#)^^#)^^#)^^#4
  1849.  
  1850.  
  1851.  
  1852. ...
  1853.  
  1854.  
  1855.  
  1856. triple-terrible tethrathoth = E100(((#^^#)^^#)^^#)^^#100
  1857.  
  1858.  
  1859.  
  1860. ...
  1861.  
  1862.  
  1863.  
  1864.  
  1865.  
  1866.  
  1867. Tethriterator Group
  1868.  
  1869. (also Great and Terrible Tethrathoth)
  1870.  
  1871.  
  1872.  
  1873.  
  1874.  
  1875. ... at ninety-nine-ex-terrible tethrathoth we reach the tethrathoth ba'al. This is where I reached the end of LECEN previously and where the set of delimiters reached its breaking point. However we now have a complete system for continuing through all the hyper-operations. We simply use a carrot top to denote the number of applications of the '^^#' operator to '#'. I will also rechrisen this number in order for it to be more extensible. Here is the new definition and name...
  1876.  
  1877.  
  1878.  
  1879. tethriterator = E100#^^#>#100
  1880.  
  1881. (also tethrathoth ba'al)
  1882.  
  1883.  
  1884.  
  1885. This number is now called the tethriterator (tetration + iterator), since it's delimiter iteratesthe smallest tetrational operator. With this new name it is now trivial to continue...
  1886.  
  1887.  
  1888.  
  1889. grand tethriterator = E100#^^#>#100#2
  1890.  
  1891. (also Great and Terrible tethrathoth)
  1892.  
  1893.  
  1894.  
  1895. double grand tethriterator = E100#^^#>#100#3
  1896.  
  1897.  
  1898.  
  1899. triple grand tethriterator = E100#^^#>#100#4
  1900.  
  1901.  
  1902.  
  1903. quadruple grand tethriterator = E100#^^#>#100#5
  1904.  
  1905.  
  1906.  
  1907. quintuple grand tethriterator = E100#^^#>#100#6
  1908.  
  1909.  
  1910.  
  1911. sextuple grand tethriterator = E100#^^#>#100#7
  1912.  
  1913.  
  1914.  
  1915. septuple grand tethriterator = E100#^^#>#100#8
  1916.  
  1917.  
  1918.  
  1919. octuple grand tethriterator = E100#^^#>#100#9
  1920.  
  1921.  
  1922.  
  1923. Aarex extended this series up to the 7th member, sextuple grand tethriterator, but this series is much more logically constructed and far easier to extend. It's also a trivial extension in any case as it is just the tethriterator sequence. We can easily jump to the hundred and first member of this sequence, and there are now a few ways to construct a name for it...
  1924.  
  1925.  
  1926.  
  1927. centuple grand tethriterator = E100#^^#>#100#101
  1928.  
  1929.  
  1930.  
  1931. In fact the -carta- operator can easily be used to extend much further and more generally. In fact we can quickly beat anything using tethrathoth, along with the terrible- and -ex- operators. Here are some examples of how our notation easily overcomes this now:
  1932.  
  1933.  
  1934.  
  1935. tethrathoth = E100#^^#>#1 = E100#^^#100
  1936.  
  1937.  
  1938.  
  1939. terrible tethrathoth = E100#^^#>#2 = E100(#^^#)^^#100
  1940.  
  1941.  
  1942.  
  1943. terrible terrible tethrathoth = E100#^^#>#3 = E100(#^^#)^^#)^^#100
  1944.  
  1945.  
  1946.  
  1947. three-ex-terrible tethrathoth = E100#^^#>#4
  1948.  
  1949.  
  1950.  
  1951. ...
  1952.  
  1953.  
  1954.  
  1955. hundred-ex-terrible tethrathoth = E100#^^#>#101
  1956.  
  1957.  
  1958.  
  1959. googol-ex-terrible tethrathoth = E100#^^#>#(1+E100)
  1960.  
  1961.  
  1962.  
  1963. ...
  1964.  
  1965.  
  1966.  
  1967. tethrathoth-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#100)
  1968.  
  1969. (~ E100#^^#>#100#2)
  1970.  
  1971.  
  1972.  
  1973. tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth
  1974.  
  1975.  
  1976.  
  1977. = E100#^^#>#(1+E100#^^#>#(1+E100#^^#100))
  1978.  
  1979. (~E100#^^#>#100#3)
  1980.  
  1981.  
  1982.  
  1983.  
  1984. ... the largest extension using this idea is found on my Ultimate Large Number List Part II. Namely ...
  1985.  
  1986.  
  1987.  
  1988.  
  1989. tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth
  1990.  
  1991.  
  1992.  
  1993.  
  1994. ... This amounts to exactly...
  1995.  
  1996.  
  1997.  
  1998.  
  1999.  
  2000. E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#100)))))))))))))))))))))))))))))))))))))))))))))))))))))
  2001.  
  2002.  
  2003.  
  2004.  
  2005. ... this precise value does not admit of a compact form even in extended Cascading-E Notation (xE^), yet it does not extend LECEN as far as it might at first seem. All those +1s barely account for anything. One can delete all of them, and replace only the deepest nested one with +2, and still get a phenomenally larger value...
  2006.  
  2007.  
  2008.  
  2009.  
  2010. E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(2+E100#^^#>#100)))))))))))))))))))))))))))))))))))))))))))))))))))))
  2011.  
  2012.  
  2013.  
  2014. ... this expression can be made more compact, using the rules of xE^...
  2015.  
  2016.  
  2017.  
  2018.  
  2019.  
  2020. E100#^^#>#(2+E100#^^#>#100)#53
  2021.  
  2022.  
  2023.  
  2024.  
  2025. ... this is still smaller than replacing 2+E100#^^#>#100 with E100#^^#>#100#2, which is much much larger...
  2026.  
  2027.  
  2028.  
  2029.  
  2030. E100#^^#>#(E100#^^#>#100#2)#53
  2031.  
  2032.  
  2033.  
  2034.  
  2035. ... this in turn can be simplified further...
  2036.  
  2037.  
  2038.  
  2039.  
  2040.  
  2041. E100#^^#>#(E100#^^#>#100#2)#53
  2042.  
  2043.  
  2044.  
  2045.  
  2046. = E100#^^#>#(E100#^^#>#(E100#^^#>#100))#53
  2047.  
  2048.  
  2049.  
  2050.  
  2051. = E100#^^#>#100#55
  2052.  
  2053.  
  2054.  
  2055.  
  2056. ... as you can see, nesting the "-ex-terrible" operator barely registers in the grander scheme of xE^. This only accounts for a single additional level of primitive recursion.grangol-carta-tethriterator (E100#^^#>#100#100), is larger than even this, and grangol-carta-tethriterator pales in comparison to what comes next...
  2057.  
  2058.  
  2059.  
  2060.  
  2061.  
  2062. greagol-carta-tethriterator = E100#^^#>#100#100#100
  2063.  
  2064.  
  2065.  
  2066.  
  2067. ... this would be like having a function which takes tethrathoth-ex-terrible tethrathoth-ex-terrible ... -ex-terrible tethrathoth, and then returned an expression with THAT many occurences of ex-terrible. Now repeat that a hundred times. This is only two levels of primitive recursion above LECEN. Going much further still we have ...
  2068.  
  2069.  
  2070.  
  2071. gigangol-carta-tethriterator = E100#^^#>#100#100#100#100
  2072.  
  2073.  
  2074.  
  2075. ...
  2076.  
  2077.  
  2078.  
  2079. gugolda-carta-tethriterator = E100#^^#>#100##100
  2080.  
  2081.  
  2082.  
  2083. ...
  2084.  
  2085.  
  2086.  
  2087. godgahlah-carta-tethriterator = E100#^^#>#100#^#100
  2088.  
  2089.  
  2090.  
  2091. grand godgahlah-carta-tethriterator = E100#^^#>#100#^#100#2
  2092.  
  2093.  
  2094.  
  2095. = E100#^^#>#100#^#(godgahlah-carta-tehtriterator)
  2096.  
  2097.  
  2098.  
  2099. ...
  2100.  
  2101.  
  2102.  
  2103. gridgahlah-carta-tethriterator = E100#^^#>#100#^##100
  2104.  
  2105.  
  2106.  
  2107. ...
  2108.  
  2109.  
  2110.  
  2111. godgathor-carta-tethriterator = E100#^^#>#100#^#^#100
  2112.  
  2113.  
  2114.  
  2115. ...
  2116.  
  2117.  
  2118.  
  2119. gralgathor-carta-tethriterator = E100#^^#>#100#^#^##100
  2120.  
  2121.  
  2122.  
  2123. ...
  2124.  
  2125.  
  2126.  
  2127. tethrathoth-carta-tethriterator = E100#^^#>#100#^^#100
  2128.  
  2129.  
  2130.  
  2131. ...
  2132.  
  2133.  
  2134.  
  2135. tethrathoth-dopplux-carta-tethriterator = E100#^^#>#100(#^^#)^(#^^#)100
  2136.  
  2137.  
  2138.  
  2139. Monster-Giant-carta-tethriterator = E100#^^#>#100(#^^#)^(#^^#)^#100
  2140.  
  2141.  
  2142.  
  2143. tethrathoth-trepplux-carta-tethriterator = E100#^^#>#100(#^^#)^^#3
  2144.  
  2145.  
  2146.  
  2147. tethrathoth-quadruplux-carta-tethriterator = E100#^^#>#100(#^^#)^^#4
  2148.  
  2149.  
  2150.  
  2151. ...
  2152.  
  2153.  
  2154.  
  2155.  
  2156.  
  2157. terrible tethrathoth-carta-tethriterator = E100#^^#>#100(#^^#)^^#100
  2158.  
  2159.  
  2160.  
  2161.  
  2162. terrible terrible tethrathoth-carta-tethriterator = E100#^^#>#100((#^^#)^^#)^^#100
  2163.  
  2164.  
  2165.  
  2166.  
  2167. ...
  2168.  
  2169.  
  2170.  
  2171.  
  2172. .... this brings us to tethriterator-carta-tethriterator or ...
  2173.  
  2174.  
  2175.  
  2176.  
  2177.  
  2178. tethritertri = E100#^^#>#100#^^#>#100
  2179.  
  2180.  
  2181.  
  2182.  
  2183. tethritertet = E100#^^#>#100#^^#>#100#^^#>#100 = E100#^^#>#*#4
  2184.  
  2185.  
  2186.  
  2187.  
  2188. tethriterpent = E100#^^#>#*#5
  2189.  
  2190.  
  2191.  
  2192.  
  2193. tethriterhex = E100#^^#>#*#6
  2194.  
  2195.  
  2196.  
  2197.  
  2198. tethriterhept = E100#^^#>#*#7
  2199.  
  2200.  
  2201.  
  2202.  
  2203. tethriteroct = E100#^^#>#*#8
  2204.  
  2205.  
  2206.  
  2207.  
  2208. tethriterenn = E100#^^#>#*#9
  2209.  
  2210.  
  2211.  
  2212.  
  2213. tethriterdeck = E100#^^#>#*#10
  2214.  
  2215.  
  2216.  
  2217.  
  2218. ...
  2219.  
  2220.  
  2221.  
  2222.  
  2223. tethriterhecate = E100#^^#>#*#100
  2224.  
  2225. (also tethritera-by-hyperion)
  2226.  
  2227.  
  2228.  
  2229.  
  2230. ... this brings us to a whole new level...
  2231.  
  2232.  
  2233.  
  2234.  
  2235.  
  2236.  
  2237.  
  2238.  
  2239. tethritera-by-deutero-hyperion = E100#^^#>#*##100
  2240.  
  2241.  
  2242.  
  2243.  
  2244. tethritera-by-trito-hyperion = E100#^^#>#*###100
  2245.  
  2246.  
  2247.  
  2248.  
  2249. tethritera-by-teterto-hyperion = E100#^^#>#*####100
  2250.  
  2251.  
  2252.  
  2253.  
  2254. tethritera-by-pepto-hyperion = E100#^^#>#*#^#5
  2255.  
  2256.  
  2257.  
  2258.  
  2259. tethritera-by-exto-hyperion = E100#^^#>#*#^#6
  2260.  
  2261.  
  2262.  
  2263.  
  2264. tethritera-by-epto-hyperion = E100#^^#>#*#^#7
  2265.  
  2266.  
  2267.  
  2268.  
  2269. tethritera-by-ogdo-hyperion = E100#^^#>#*#^#8
  2270.  
  2271.  
  2272.  
  2273.  
  2274. tethritera-by-ento-hyperion = E100#^^#>#*#^#9
  2275.  
  2276.  
  2277.  
  2278.  
  2279. tethritera-by-dekato-hyperion = E100#^^#>#*#^#10
  2280.  
  2281.  
  2282.  
  2283.  
  2284. ...
  2285.  
  2286.  
  2287.  
  2288.  
  2289. tethritera-by-hyperada-hyperion = E100#^^#>#*#^#100
  2290.  
  2291.  
  2292.  
  2293.  
  2294. tethritera-by-hyperada-hyperion-by-hyperion = E100#^^#>#*#^#*#100
  2295.  
  2296.  
  2297.  
  2298.  
  2299. tethritera-by-hyperada-hyperion-by-deutero-hyperion = E100#^^#>#*#^#*##100
  2300.  
  2301.  
  2302.  
  2303.  
  2304. tethritera-by-hyperada-hyperion-by-trito-hyperion = E100#^^#>#*#^#*###100
  2305.  
  2306.  
  2307.  
  2308.  
  2309. tethritera-by-hyperada-hyperion-by-teterto-hyperion = E100#^^#>#*#^#*####100
  2310.  
  2311.  
  2312.  
  2313.  
  2314. ...
  2315.  
  2316.  
  2317.  
  2318.  
  2319. tethritera-by-hyperada-hyperion-by-hyperada-hyperion = E100#^^#>#*#^#*#^#100
  2320.  
  2321.  
  2322.  
  2323.  
  2324. ...
  2325.  
  2326.  
  2327.  
  2328.  
  2329. tethritera-by-hyperada-deutero-hyperion = E100#^^#>#*#^##100
  2330.  
  2331.  
  2332.  
  2333.  
  2334. tethritera-by-hyperada-trito-hyperion = E100#^^#>#*#^###100
  2335.  
  2336.  
  2337.  
  2338.  
  2339. tethritera-by-hyperada-teterto-hyperion = E100#^^#>#*#^####100
  2340.  
  2341.  
  2342.  
  2343.  
  2344. tethritera-by-hyperada-pepto-hyperion = E100#^^#>#*#^#^#5
  2345.  
  2346.  
  2347.  
  2348.  
  2349. tethritera-by-hyperada-exto-hyperion = E100#^^#>#*#^#^#6
  2350.  
  2351.  
  2352.  
  2353.  
  2354. tethritera-by-hyperada-epto-hyperion = E100#^^#>#*#^#^#7
  2355.  
  2356.  
  2357.  
  2358.  
  2359. tethritera-by-hyperada-ogdo-hyperion = E100#^^#>#*#^#^#8
  2360.  
  2361.  
  2362.  
  2363.  
  2364. tethritera-by-hyperada-ento-hyperion = E100#^^#>#*#^#^#9
  2365.  
  2366.  
  2367.  
  2368.  
  2369. tethritera-by-hyperada-dekato-hyperion = E100#^^#>#*#^#^#10
  2370.  
  2371.  
  2372.  
  2373.  
  2374. ...
  2375.  
  2376.  
  2377.  
  2378.  
  2379. tethritera-by-hyperada-hyperada-hyperion = E100#^^#>#*#^#^#100
  2380.  
  2381. (also tethritera-by-hyperada-hecato-hyperion)
  2382.  
  2383. (also tethritera-by-hyper-tetradatri)
  2384.  
  2385.  
  2386.  
  2387.  
  2388. tethritera-by-hyper-tetradatet = E100#^^#>#*#^#^#^#100
  2389.  
  2390.  
  2391.  
  2392.  
  2393. tethritera-by-hyper-tetradapent = E100#^^#>#*#^^#5
  2394.  
  2395.  
  2396.  
  2397.  
  2398. tethritera-by-hyper-tetradahex = E100#^^#>#*#^^#6
  2399.  
  2400.  
  2401.  
  2402.  
  2403. tethritera-by-hyper-tetradahept = E100#^^#>#*#^^#7
  2404.  
  2405.  
  2406.  
  2407.  
  2408. tethritera-by-hyper-tetrada-oct = E100#^^#>#*#^^#8
  2409.  
  2410.  
  2411.  
  2412.  
  2413. tethritera-by-hyper-tetrada-enn = E100#^^#>#*#^^#9
  2414.  
  2415.  
  2416.  
  2417.  
  2418. tethritera-by-hyper-tetrada-deck = E100#^^#>#*#^^#10
  2419.  
  2420.  
  2421.  
  2422.  
  2423. ...
  2424.  
  2425.  
  2426.  
  2427.  
  2428. tethritera-by-tethrathoth = E100#^^#>#*#^^#100
  2429.  
  2430. (also tethritera-by-hyper-tetrada-hecate)
  2431.  
  2432.  
  2433.  
  2434.  
  2435. tethritera-by-terrible-tethrathoth = E100#^^#>#*(#^^#)^^#100
  2436.  
  2437.  
  2438.  
  2439.  
  2440. tethritera-by-terrible-terrible-tethrathoth = E100#^^#>#*((#^^#)^^#)^^#100
  2441.  
  2442.  
  2443.  
  2444.  
  2445. tethritera-by-triterrible-tethrathoth = E100#^^#>#*(((#^^#)^^#)^^#)^^#100
  2446.  
  2447.  
  2448.  
  2449.  
  2450. tethritera-by-tetraterrible-tethrathoth = E100#^^#>#*#^^#>#5
  2451.  
  2452.  
  2453.  
  2454.  
  2455. tethritera-by-pentaterrible-tethrathoth = E100#^^#>#*#^^#>#6
  2456.  
  2457.  
  2458.  
  2459.  
  2460. tethritera-by-hexaterrible-tethrathoth = E100#^^#>#*#^^#>#7
  2461.  
  2462.  
  2463.  
  2464.  
  2465. tethritera-by-heptaterrible-tethrathoth = E100#^^#>#*#^^#>#8
  2466.  
  2467.  
  2468.  
  2469.  
  2470. tethritera-by-octaterrible-tethrathoth = E100#^^#>#*#^^#>#9
  2471.  
  2472.  
  2473.  
  2474.  
  2475. tethritera-by-ennaterrible-tethrathoth = E100#^^#>#*#^^#>#10
  2476.  
  2477.  
  2478.  
  2479.  
  2480. tethritera-by-dekaterrible-tethrathoth = E100#^^#>#*#^^#>#11
  2481.  
  2482.  
  2483.  
  2484.  
  2485. ...
  2486.  
  2487.  
  2488.  
  2489.  
  2490. deutero-tethriterator = E100#^^#>#*#^^#>#100
  2491.  
  2492. (also tethritera-tethriterator)
  2493.  
  2494. (also tethritera-by-hectaterrible-tethrathoth)
  2495.  
  2496.  
  2497.  
  2498.  
  2499. ... this brings us to yet another higher level of diagonalization, still within thetethriterator group...
  2500.  
  2501.  
  2502.  
  2503.  
  2504.  
  2505. trito-tethriterator = E100#^^#>#*#^^#>#*#^^#>#100
  2506.  
  2507.  
  2508.  
  2509.  
  2510. teterto-tethriterator = E100#^^#>#*#^^#>#*#^^#>#*#^^#>#100
  2511.  
  2512.  
  2513.  
  2514.  
  2515. pepto-tethriterator = E100(#^^#>#)^#5
  2516.  
  2517.  
  2518.  
  2519.  
  2520. exto-tethriterator = E100(#^^#>#)^#6
  2521.  
  2522.  
  2523.  
  2524.  
  2525. epto-tethriterator = E100(#^^#>#)^#7
  2526.  
  2527.  
  2528.  
  2529.  
  2530. ogdo-tethriterator = E100(#^^#>#)^#8
  2531.  
  2532.  
  2533.  
  2534.  
  2535. ento-tethriterator = E100(#^^#>#)^#9
  2536.  
  2537.  
  2538.  
  2539.  
  2540. dekato-tethriterator = E100(#^^#>#)^#10
  2541.  
  2542.  
  2543.  
  2544.  
  2545. ...
  2546.  
  2547.  
  2548.  
  2549.  
  2550. isosto-tethriterator = E100(#^^#>#)^#20
  2551.  
  2552.  
  2553.  
  2554.  
  2555. ...
  2556.  
  2557.  
  2558.  
  2559.  
  2560. hecato-tethriterator = E100(#^^#>#)^#100
  2561.  
  2562.  
  2563.  
  2564.  
  2565. ... next an even faster sequence ...
  2566.  
  2567.  
  2568.  
  2569.  
  2570.  
  2571. tethriterchain = E100(#^^#>#)^#100
  2572.  
  2573.  
  2574.  
  2575.  
  2576. tethritergrid = E100(#^^#>#)^##100
  2577.  
  2578.  
  2579.  
  2580.  
  2581. tethritercube = E100(#^^#>#)^###100
  2582.  
  2583.  
  2584.  
  2585.  
  2586. tethriterquarticate = E100(#^^#>#)^####100
  2587.  
  2588.  
  2589.  
  2590.  
  2591. tethriterquinticate = E100(#^^#>#)^#^#5
  2592.  
  2593.  
  2594.  
  2595.  
  2596. tethritersexticate = E100(#^^#>#)^#^#6
  2597.  
  2598.  
  2599.  
  2600.  
  2601. tethritersepticate = E100(#^^#>#)^#^#7
  2602.  
  2603.  
  2604.  
  2605.  
  2606. tethriterocticate = E100(#^^#>#)^#^#8
  2607.  
  2608.  
  2609.  
  2610.  
  2611. tethriternonicate = E100(#^^#>#)^#^#9
  2612.  
  2613.  
  2614.  
  2615.  
  2616. tethriterdecicate = E100(#^^#>#)^#^#10
  2617.  
  2618.  
  2619.  
  2620.  
  2621. ...
  2622.  
  2623.  
  2624.  
  2625.  
  2626. tethriterviginticate = E100(#^^#>#)^#^#20
  2627.  
  2628.  
  2629.  
  2630.  
  2631. tethritertriginticate = E100(#^^#>#)^#^#30
  2632.  
  2633.  
  2634.  
  2635.  
  2636. tethriterquadraginticate = E100(#^^#>#)^#^#40
  2637.  
  2638.  
  2639.  
  2640.  
  2641. tethriterquinquaginticate = E100(#^^#>#)^#^#50
  2642.  
  2643.  
  2644.  
  2645.  
  2646. tethritersexaginticate = E100(#^^#>#)^#^#60
  2647.  
  2648.  
  2649.  
  2650.  
  2651. tethriterseptuaginticate = E100(#^^#>#)^#^#70
  2652.  
  2653.  
  2654.  
  2655.  
  2656. tethriteroctoginticate = E100(#^^#>#)^#^#80
  2657.  
  2658.  
  2659.  
  2660.  
  2661. tethriternonaginticate = E100(#^^#>#)^#^#90
  2662.  
  2663.  
  2664.  
  2665.  
  2666. tethritercenticate = E100(#^^#>#)^#^#100
  2667.  
  2668.  
  2669.  
  2670.  
  2671. ... next on to even more gargantuan numbers ...
  2672.  
  2673.  
  2674.  
  2675.  
  2676.  
  2677. tethritergodgathor = E100(#^^#>#)^#^#100
  2678.  
  2679.  
  2680.  
  2681.  
  2682. tethritergralgathor = E100(#^^#>#)^#^##100
  2683.  
  2684.  
  2685.  
  2686.  
  2687. tethritergodtothol = E100(#^^#>#)^#^#^#100
  2688.  
  2689.  
  2690. tethritertethrathoth = E100(#^^#>#)^#^^#100
  2691.  
  2692. tethriter-Monster-Giant = E100(#^^#>#)^(#^^#)^#100
  2693.  
  2694. tethriter-terri-tethrathoth = E100(#^^#>#)^(#^^#)^^#100
  2695.  
  2696. tethriter-duterri-tethrathoth = E100(#^^#>#)^((#^^#)^^#)^^#100
  2697.  
  2698. tethriter-triterri-tethrathoth = E100(#^^#>#)^(#^^#>#)4
  2699.  
  2700. tethriterator-dopplux = E100(#^^#>#)^(#^^#>#)100
  2701.  
  2702. tethriterator-trepplux = E100(#^^#>#)^^#3
  2703.  
  2704. tethriterator-quadrupplux = E100(#^^#>#)^^#4
  2705.  
  2706. terrible tethriterator = E100(#^^#>#)^^#100
  2707.  
  2708. terrible terrible tethriterator = E100((#^^#>#)^^#)^^#100
  2709.  
  2710. terrible terrible terrible tethriterator = E100(((#^^>#)^^#)^^#)^^#100
  2711.  
  2712. terrible terrible terrible terrible tethriterator = E100((((#^^#>#)^^#)^^#)^^#)^^#100
  2713.  
  2714. ...
  2715.  
  2716. Now imagine the number ...
  2717.  
  2718. E100(((...(((#^^#>#)^^#)^^#)^^# ... ^^#)^^#)^^#100 w/100 ^^#s
  2719.  
  2720. using xE^ we can now truncate this to...
  2721.  
  2722. E100#^^#>(#+#)100
  2723.  
  2724. This brings us to the next level of recursion. We can begin to stack larger and larger hyperion expression on top of #^^#. Here we go ...
  2725.  
  2726. tethriditerator = E100#^^#>(#+#)100
  2727.  
  2728. tethritriterator = E100#^^#>(#+#+#)100
  2729.  
  2730. tethriquaditerator = E100#^^#>(#+#+#+#)100
  2731.  
  2732. tethriquiditerator = E100#^^#>##5
  2733.  
  2734. tethrisiditerator = E100#^^#>##6
  2735.  
  2736. tethrisepiterator = E100#^^#>##7
  2737.  
  2738. tethriogditerator = E100#^^#>##8
  2739.  
  2740. tethrinoniterator = E100#^^#>##9
  2741.  
  2742. tethrideciterator = E100#^^#>##10
  2743.  
  2744. ...
  2745.  
  2746. ... even higher diagonalizations ...
  2747.  
  2748. tethrigriditerator = E100#^^#>##100
  2749.  
  2750. tethricubiculator = E100#^^#>###100
  2751.  
  2752. tethriquarticulator = E100#^^#>####100
  2753.  
  2754. tethriquinticulator = E100#^^#>#^#5
  2755.  
  2756. tethrisexticulator = E100#^^#>#^#6
  2757.  
  2758. tethrisepticulator = E100#^^#>#^#7
  2759.  
  2760. tethriocticulator = E100#^^#>#^#8
  2761.  
  2762. tethrinoniculator = E100#^^#>#^#9
  2763.  
  2764. tethrideciculator = E100#^^#>#^#10
  2765.  
  2766. ...
  2767.  
  2768. tethricenticulator = E100#^^#>#^#100
  2769.  
  2770. ... meanwhile in the next next dimension ...
  2771.  
  2772. tethrispatialator = E100#^^#>#^#100
  2773.  
  2774. tethrispatial-squarediterator = E100#^^#>(#^#*#^#)100
  2775.  
  2776. tethrispatial-cubiculator = E100#^^#>(#^#*#^#*#^#)100
  2777.  
  2778. tethrispatial-quarticulator = E100#^^#>(#^#*#^#*#^#*#^#)100
  2779.  
  2780. tethrispatial-quinticulator = E100#^^#>#^##5
  2781.  
  2782. tethrispatial-sexticulator = E100#^^#>#^##6
  2783.  
  2784. tethrispatial-septiculator = E100#^^#>#^##7
  2785.  
  2786. tethrispatial-octiculator = E100#^^#>#^##8
  2787.  
  2788. tethrispatial-noniculator = E100#^^#>#^##9
  2789.  
  2790. tethrispatial-deciculator = E100#^^#>#^##10
  2791.  
  2792. tethrispatial-centiculator = E100#^^#>#^##100
  2793.  
  2794. ... we still have quite a climb left to reach #^^## ...
  2795.  
  2796. tethrideuterspatialator = E100#^^#>#^##100
  2797.  
  2798. tethritritospatialator = E100#^^#>#^###100
  2799.  
  2800. tethritetertospatialator = E100#^^#>#^####100
  2801.  
  2802. tethripeptospatialator = E100#^^#>#^#^#5
  2803.  
  2804. tethri-extospatialator = E100#^^#>#^#^#6
  2805.  
  2806. tethri-eptospatialator = E100#^^#>#^#^#7
  2807.  
  2808. tethri-ogdospatialator = E100#^^#>#^#^#8
  2809.  
  2810. tethri-entospatialator = E100#^^#>#^#^#9
  2811.  
  2812. tethri-dekatospatialator = E100#^^#>#^#^#10
  2813.  
  2814. ...
  2815.  
  2816. tethri-isostospatialator = E100#^^#>#^#^#20
  2817.  
  2818. ...
  2819.  
  2820. tethri-hecatospatialator = E100#^^#>#^#^#100
  2821.  
  2822. ... and another even higher level of diagonalization ...
  2823.  
  2824. tethri-superspatialator = E100#^^#>#^#^#100
  2825.  
  2826. tethri-quadratetratediterator = E100#^^#>#^#^#^#100
  2827.  
  2828. tethri-quintatetratediterator = E100#^^#>#^^#5
  2829.  
  2830. tethri-sextatetratediterator = E100#^^#>#^^#6
  2831.  
  2832. tethri-septatetratediterator = E100#^^#>#^^#7
  2833.  
  2834. tethri-octatetratediterator = E100#^^#>#^^#8
  2835.  
  2836. tethri-nonatetratediterator = E100#^^#>#^^#9
  2837.  
  2838. tethri-decatetratediterator = E100#^^#>#^^#10
  2839.  
  2840. ...
  2841.  
  2842. tethri-vigintatetratediterator = E100#^^#>#^^#20
  2843.  
  2844. ...
  2845.  
  2846. tethri-centatetratediterator = E100#^^#>#^^#100
  2847.  
  2848. In a very loose sense we can think of this as a double stack tetrational tower. ' #^^#>#^^# ' can be interpreted as #^^(#+#), and thus as the hypothetical ordinal w^^(w*2). However do not mistake this for a mere #^^200. That value can easily be defined as E100#^^#200 = E100#^^#[200]100 = E100#^^(200)100. That value however is already vastly smaller than a grand tethrathoth, which is E100#^^(tethrathoth)100. Remember that ordinal hyper-operations are far more complex than the hyper-operations applied to the integers! Tethri-centatetratediterator would first have to expand the #^^# on top of the stack. This must then decompose into iterations of the ^^# operator on yet smaller hyperials. A hyperial is an ordinal written using hyperions and hyperion operators. Let's look at some of the expansion...
  2849.  
  2850.  
  2851. E100#^^#>#^^#100 =
  2852.  
  2853. E100#^^#>#^^(100)100 =
  2854.  
  2855. E100#^^#>#^#^ ... ^#^#^#100 =
  2856.  
  2857. E100#^^#>#^#^ ... ^#^#100100 =
  2858.  
  2859. E100#^^#>#^#^ ... ^(#^#99*#^#99* ... #^#99*#^#99)100 =
  2860.  
  2861. E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)100)100 =
  2862.  
  2863. E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99*(#^#97)100)100 =
  2864.  
  2865. ...
  2866.  
  2867. = E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99* ... *(#^#2)99*(#^#)99*#^#)100 =
  2868.  
  2869. E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99* ... *(#^#2)99*(#^#)99*#100)100
  2870.  
  2871. ... at this point the decomposition cascades down to the next level although much more complex than before. You'll notice that the decomposition follows very similar behavior to the goodstein sequence. The decomposition here is also identical to that of #^^# in a tethrathoth. However once this collapse reaches the form &*#, we do not simply expand using the expansion rule as in tethrathoth. Instead we aren't even done collapsing the hyperial above the stack. It proceeds as follows:
  2872.  
  2873.  
  2874. E100#^^#>(&*#)100 =
  2875.  
  2876. E100#^^#>(&+&+&+ ... +&+&+&)100 w/100 &s
  2877.  
  2878. ... now & must itself decompose into a series of additions. This continues for a very long time until we eventually reachthe form &+#. At this point we get...
  2879.  
  2880.  
  2881. E100#^^#>(&+#)100 =
  2882.  
  2883. E100(#^^#>&)^^#>#100 =
  2884.  
  2885. E100(#^^#>&)^^#>(100)100 =
  2886.  
  2887. E100(((...(((#^^#>&)^^#)^^#)^^#) ... )^^#)^^#)^^#100 w/100 ^^#s after #^^#>&
  2888.  
  2889. the decomposition of & temporarily halts here as the ^^# need to be resolved first. This leads to a massive power tower, which keeps growing and growing as ^^# operators are resolved. This goes on while & further expands into even more ^^# operators. Finally at the pinnacle of this unfathomably larger tower would be #^^# ... but then the real nightmare has only begun as the entire super-cascade itself made up of cascading components must very slowly decay. The process becomes hazy out there but what we do know is thateventually it must reduce to (#^^#)^& for some extremely complicated and long winded &. Please note that & is NOT a number but a hyperiate. It will also NOT be something "simple" like (#^^#)^(#^^#)^(#^^#)^...^(#^^#)^(#^^#) with a huge number of #^^#s. The delimiter we'll rather involve a lot of mixed expressions. Generally speaking things will get frighteningly complicated before they become simple and repetitive. This only happens whenever we get to apply the recursive rule. This is the rule that actually increases the size of the last argument. Of coarse the last argument will continue to return to the value of 100 because the first argument is 100. The huge value then get's stored in the delimiter by the number of repetitions until it feeds back into the last argument. The processes are far too long for us to ever have a complete picture of it. However we can at least know that it will return to certain forms which we can describe. eventually we would reach...
  2890.  
  2891. E100#^^#X
  2892.  
  2893. where X is a tremendous value, virtually indistinguishable for mere mortals such as us fromtehtri-centatetratediterator itself! Suffice it to say that X is MUCH MUCH bigger than 200!
  2894.  
  2895. We STILL have not reached #^^##! Let's continue. We now introduce an even higher level of diagonalization, by introducing the staculate operator ...
  2896.  
  2897. staculated-tethrathoth = E100#^^#>#^^#100
  2898.  
  2899. staculated-terrible-tethrathoth = E100#^^#>(#^^#)^^#100
  2900.  
  2901. staculated-double-terrible-tethrathoth = E100#^^#>((#^^#)^^#)^^#100
  2902.  
  2903. ...
  2904.  
  2905. staculated-tethriterator = E100#^^#>#^^#>#100
  2906.  
  2907. note that the second caret top must be resolved before the first. Moving on we have...
  2908.  
  2909. terrible staculated-tethriterator = E100(#^^#>#^^#>#)^^#100
  2910.  
  2911. double terrible staculated-tethriterator = E100((#^^#>#^^#>#)^^#)^^#100
  2912.  
  2913. ...
  2914.  
  2915. hundred-ex-terrible staculated-tethriterator = E100#^^#>(#^^#>#+#)100
  2916.  
  2917. ...
  2918.  
  2919. E100#^^#>(#^^#>#+#^^#>#)100
  2920.  
  2921. staculated-deutero-tethriterator = E100#^^#>(#^^#>#*#^^#>#)100
  2922.  
  2923. staculated-trito-tethriterator = E100#^^#>(#^^#>#)^#3
  2924.  
  2925. staculated-teterto-tethriterator = E100#^^#>(#^^#>#)^#4
  2926.  
  2927. ...
  2928.  
  2929. staculated-hecato-tethriterator = E100#^^#>(#^^#>#)^#100
  2930.  
  2931. ...
  2932.  
  2933. staculated-terrible-tethriterator = E100#^^#>(#^^#>#)^^#100
  2934.  
  2935. staculated-double-terrible-tethriterator = E100#^^#>((#^^#>#)^^#)^^#100
  2936.  
  2937. ...
  2938.  
  2939. staculated-tethriditerator = E100#^^#>#^^#>(#+#)100
  2940.  
  2941. staculated-tethritriterator = E100#^^#>#^^#>(#+#+#)100
  2942.  
  2943. staculated-tethriquaditerator = E100#^^#>#^^#>(#+#+#+#)100
  2944.  
  2945. staculated-tethriquiditerator = E100#^^#>#^^#>##5
  2946.  
  2947. staculated-tethrisiditerator = E100#^^#>#^^#>##6
  2948.  
  2949. staculated-tethrisepiterator = E100#^^#>#^^#>##7
  2950.  
  2951. staculated-tethri-ogditerator = E100#^^#>#^^#>##8
  2952.  
  2953. staculated-tethri-noniterator = E100#^^#>#^^#>##9
  2954.  
  2955. staculated-tethri-deciterator = E100#^^#>#^^#>##10
  2956.  
  2957.  
  2958. ...
  2959.  
  2960. staculated-tethrigriditerator = E100#^^#>#^^#>##100
  2961.  
  2962. staculated-tethricubiculator = E100#^^#>#^^#>###100
  2963.  
  2964. staculated-tethriquarticulator = E100#^^#>#^^#>####100
  2965.  
  2966. staculated-tethriquinticulator = E100#^^#>#^^#>#^#5
  2967.  
  2968. staculated-tethrisexticulator = E100#^^#>#^^#>#^#6
  2969.  
  2970. staculated-tethrisepticulator = E100#^^#>#^^#>#^#7
  2971.  
  2972. staculated-tethri-octiculator = E100#^^#>#^^#>#^#8
  2973.  
  2974. staculated-tethrinoniculator = E100#^^#>#^^#>#^#9
  2975.  
  2976. staculated-tethrideciculator = E100#^^#>#^^#>#^#10
  2977.  
  2978. ...
  2979.  
  2980. staculated-tethrispatialator = E100#^^#>#^^#>#^#100
  2981.  
  2982. staculated-tethrideuterspatialator = E100#^^#>#^^#>#^##100
  2983.  
  2984. staculated-tethritritospatialator = E100#^^#>#^^#>#^###100
  2985.  
  2986. staculated-tethritetertospatialator = E100#^^#>#^^#>#^####100
  2987.  
  2988. ...
  2989.  
  2990. staculated-tethri-superspatialator = E100#^^#>#^^#>#^#^#100
  2991.  
  2992. staculated-tethriquadratetratediterator = E100#^^#>#^^#>#^#^#^#100
  2993.  
  2994. staculated-tethriquintatetratediterator = E100#^^#>#^^#>#^^#5
  2995.  
  2996. staculated-tethrisextatetratediterator = E100#^^#>#^^#>#^^#6
  2997.  
  2998. staculated-tethriseptatetratediterator = E100#^^#>#^^#>#^^#7
  2999.  
  3000. staculated-tethrioctatetratediterator = E100#^^#>#^^#>#^^#8
  3001.  
  3002. staculated-tethrinonatetratediterator = E100#^^#>#^^#>#^^#9
  3003.  
  3004. staculated-tethridecatetratediterator = E100#^^#>#^^#>#^^#10
  3005.  
  3006. Here we reach the end of the tethriterator group. We are now in need of something more extensible...
  3007.  
  3008.  
  3009. Tethrato Group
  3010.  
  3011. Next we establish ' tethrato ' as the general root for a tetrational operator. Here are some new constructions for continuing along the main sequence of xE^:
  3012.  
  3013. troiturreted-tethrathoth = E100#^^#>#^^#>#^^#100
  3014.  
  3015. territethraturreted-sur-duturreted-tethrathoth = E100#^^#>#^^#>(#^^#)^^#100
  3016.  
  3017. tethriterata-turreted-sur-duturreted-tethrathoth = E100#^^#>#^^#>#^^#>#100
  3018.  
  3019. ...
  3020.  
  3021. quatreturreted-tethrathoth = E100#^^#>#^^#>#^^#>#^^#100
  3022.  
  3023. tethriterata-turreted-sur-troiturreted-tethrathoth = E100#^^#>#^^#>#^^#>#^^#>#100
  3024.  
  3025. cinqturreted-tethrathoth = E100#^^##5
  3026.  
  3027. sesturreted-tethrathoth = E100#^^##6
  3028.  
  3029. septurreted-tethrathoth = E100#^^##7
  3030.  
  3031. huiturreted-tethrathoth = E100#^^##8
  3032.  
  3033. neufturreted-tethrathoth = E100#^^##9
  3034.  
  3035. dexturreted-tethrathoth = E100#^^##10
  3036.  
  3037. ...
  3038.  
  3039. Berlin Wall = E100#^^##100,000,000 =
  3040.  
  3041. E100#^^#>#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#>#^^#100
  3042.  
  3043. w/100,000,000 #^^#s
  3044.  
  3045. ... this expression would be roughly 7 to 8 times the length of the real berlin wall which stretched for about 100 miles ...
  3046.  
  3047. grand Berlin Wall = E100#^^##100,000,000#2 =
  3048.  
  3049. E100#^^##(E100#^^##100,000,000) = E100#^^##(Berlin Wall) =
  3050.  
  3051. E100#^^#>#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#>#^^#100
  3052.  
  3053. w/Berlin Wall #^^#s
  3054.  
  3055. ... this expression ... stretches further than the diameter of the observable universe-- no scratch that, scale up from the Berlin Wall to the observable universe as many times as there are particles in the observable universe -- no scratch that, find out how many particles THAT would contain scales up that many times then find out how many particles -- ah, fuck it, we left analogies like this behind AGES ago. There is no possible way for mere mortals such as us to unpack this completely ... moving on ...
  3056.  
  3057.  
  3058.  
  3059.  
  3060. Tethrasquare Group
  3061.  
  3062.  
  3063. ... at last we reach #^^##, identified at the closing of the Cascading-E article as the foundation of formulating xE^. Before we could not provide a fundamental sequence for it. Now we can say ...
  3064.  
  3065. #^^##[n] = #^^#>#^^#>#^^#> ... >#^^#>#^^# w/n #^^#s
  3066.  
  3067. Aarex instead of giving it a fundamental sequence treated it as a mere synonym. This makes it significantly less powerful.
  3068.  
  3069. In any case we can now define the following googolism ...
  3070.  
  3071. tethrasquare = E100#^^##100
  3072.  
  3073. this expands to...
  3074.  
  3075. E100#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#100 w/100 #^^#s
  3076.  
  3077. Already we have reached the ordinal ζ0 also called φ(2,0) or ε(0,1) using my Binary Epsilon function. This is the hypothetical level of Bowers' pentational arrays ... but we've only just begun with hyperion tetration! We have merely reached the 2nd tetrational operator, the ^^##-operator. With that in mind we can go much further...
  3078.  
  3079. grand tethrasquare = E100#^^##100#2
  3080.  
  3081. grangol-carta-tethrasquare = E100#^^##100#100
  3082.  
  3083. duble-tethrasquare = E100#^^##100#^^##100
  3084.  
  3085. treble-tethrasquare = E100#^^##100#^^##100#^^##100
  3086.  
  3087. quadreble-tethrasquare = E100#^^##*#5
  3088.  
  3089. quibble-tethrasquare = E100#^^##*#6
  3090.  
  3091. sextuble-tethrasquare = E100#^^##*#7
  3092.  
  3093. septuble-tethrasquare = E100#^^##*#8
  3094.  
  3095. octuble-tethrasquare = E100#^^##*#9
  3096.  
  3097. nonuble-tethrasquare = E100#^^##*#10
  3098.  
  3099. ...
  3100.  
  3101. deutero-tethrasquare = E100#^^##*#^^##100
  3102.  
  3103. trito-tethrasquare = E100#^^##*#^^##*#^^##100
  3104.  
  3105. teterto-tethrasquare = E100#^^##*#^^##*#^^##*#^^##100
  3106.  
  3107. pepto-tethrasquare = E100(#^^##)^#5
  3108.  
  3109. exto-tethrasquare = E100(#^^##)^#6
  3110.  
  3111. epto-tethrasquare = E100(#^^##)^#7
  3112.  
  3113. ogdo-tethrasquare = E100(#^^##)^#8
  3114.  
  3115. ento-tethrasquare = E100(#^^##)^#9
  3116.  
  3117. dekato-tethrasquare = E100(#^^##)^#10
  3118.  
  3119. ...
  3120.  
  3121. isosto-tethrasquare = E100(#^^##)^#20
  3122.  
  3123. ...
  3124.  
  3125. hecato-tethrasquare = E100(#^^##)^#100
  3126.  
  3127. ...
  3128.  
  3129. terrible tethrasquare = E100(#^^##)^^#100
  3130.  
  3131. double terrible tethrasquare = E100((#^^##)^^#)^^#100
  3132.  
  3133. ...
  3134.  
  3135. hundred-ex-terrible tethrasquare = E100(#^^##)^^#>#100
  3136.  
  3137. tethrithoth-ex-terrible tethrasquare = E100(#^^##)^^#>#(E100#^^#100)
  3138.  
  3139. tethrasquare-ex-terrible tethrasquare = E100(#^^##)^^#>#(E100#^^##100)
  3140.  
  3141. ... to go further we allow previous googolism's to act as operators on newer googolism's in a way that is analogous to how xE^ takes ordinals and applies previous operators to generate new ordinals ...
  3142.  
  3143. tethriterated-tethrasquare = E100(#^^##)^^#>#100
  3144.  
  3145. grand tethriterated-tethrasquare = E100(#^^##)^^#>#100#2
  3146.  
  3147. ...
  3148.  
  3149. tethriditerated-tethrasquare = E100(#^^##)^^#>(#+#)100
  3150.  
  3151. tethritriterated-tethrasquare = E100(#^^##)^^#>(#+#+#)100
  3152.  
  3153. tethriquaditerated-tethrasquare = E100(#^^##)^^#>(#+#+#+#)100
  3154.  
  3155. tethriquiditerated-tethrasquare = E100(#^^##)^^#>##5
  3156.  
  3157. tethrisiditerated-tethrasquare = E100(#^^##)^^#>##6
  3158.  
  3159. tethrisepiterated-tethrasquare = E100(#^^##)^^#>##7
  3160.  
  3161. tethri-ogditerated-tethrasquare = E100(#^^##)^^#>##8
  3162.  
  3163. tethri-noniterated-tethrasquare = E100(#^^##)^^#>##9
  3164.  
  3165. tethri-deciterated-tethrasquare = E100(#^^##)^^#>##10
  3166.  
  3167. ...
  3168.  
  3169. tethrigriditerated-tethrasquare = E100(#^^##)^^#>##100
  3170.  
  3171. tethricubiculated-tethrasquare = E100(#^^##)^^#>###100
  3172.  
  3173. tethriquarticulated-tethrasquare = E100(#^^##)^^#>####100
  3174.  
  3175. tethriquinticulated-tethrasquare = E100(#^^##)^^#>#^#5
  3176.  
  3177. tethrisexticulated-tethrasquare = E100(#^^##)^^#>#^#6
  3178.  
  3179. tethrisepticulated-tethrasquare = E100(#^^##)^^#>#^#7
  3180.  
  3181. tethri-octiculated-tethrasquare = E100(#^^##)^^#>#^#8
  3182.  
  3183. tethrinoniculated-tethrasquare = E100(#^^##)^^#>#^#9
  3184.  
  3185. tethrideciculated-tethrasquare = E100(#^^##)^^#>#^#10
  3186.  
  3187. ...
  3188.  
  3189. tethrispatialated-tethrasquare = E100(#^^##)^^#>#^#100
  3190.  
  3191. tethrideuterspatialated-tethrasquare = E100(#^^##)^^#>#^##100
  3192.  
  3193. tethritritospatialated-tethrasquare = E100(#^^##)^^#>#^###100
  3194.  
  3195. tethritetertospatialated-tethrasquare = E100(#^^##)^^#>#^####100
  3196.  
  3197. tethripeptospatialated-tethrasquare = E100(#^^##)^^#>#^#^#5
  3198.  
  3199. tethriextospatialated-tethrasquare = E100(#^^##)^^#>#^#^#6
  3200.  
  3201. tethrieptospatialated-tethrasquare = E100(#^^##)^^#>#^#^#7
  3202.  
  3203. tethriogdospatialated-tethrasquare = E100(#^^##)^^#>#^#^#8
  3204.  
  3205. tethrientospatialated-tethrasquare = E100(#^^##)^^#>#^#^#9
  3206.  
  3207. tethridekatospatialated-tethrasquare = E100(#^^##)^^#>#^#^#10
  3208.  
  3209. ...
  3210.  
  3211. tethrisuperspatialated-tethrasquare = E100(#^^##)^^#>#^#^#100
  3212.  
  3213. tethriquadratetratediterated-tethrasquare = E100(#^^##)^^#>#^#^#^#100
  3214.  
  3215. tethriquintatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#5
  3216.  
  3217. tethrisextatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#6
  3218.  
  3219. tethriseptatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#7
  3220.  
  3221. tethrioctatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#8
  3222.  
  3223. tethrinonatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#9
  3224.  
  3225. tethridecatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#10
  3226.  
  3227. ...
  3228.  
  3229. tethricentatetratediterated-tethrasquare = E100(#^^##)^^#>#^^#100
  3230.  
  3231. ... here we reach the end at which this technique can be easily applied. Here I'll take a slight shift in gears to allow for better and more logical generalization...
  3232.  
  3233. tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#100
  3234.  
  3235. territethrastaculated-tethritertethrasquare = E100(#^^##)^^#>(#^^#)^^#100
  3236.  
  3237. ...
  3238.  
  3239. tethriterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#100
  3240.  
  3241. tethriditerstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>(#+#)100
  3242.  
  3243. tethritriterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>(#+#+#)100
  3244.  
  3245. tethriquaditerstaculated-tethritertethrasquare
  3246.  
  3247. = E100(#^^##)^^#>#^^#>(#+#+#+#)100
  3248.  
  3249. ...
  3250.  
  3251. tethrigriditerstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>##100
  3252.  
  3253. tethricubiterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>###100
  3254.  
  3255. tethriquartiterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>####100
  3256.  
  3257. ...
  3258.  
  3259. tethrispatialiterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^#100
  3260.  
  3261. tethrisuperspatialiterstaculated-tethritertethrasquare
  3262.  
  3263. = E100(#^^##)^^#>#^^#>#^#^#100
  3264.  
  3265. tethriquadratetratediterstaculated-tethritertethrasquare
  3266.  
  3267. = E100(#^^##)^^#>#^^#>#^^#4
  3268.  
  3269. tethriquintatetratediterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#5
  3270.  
  3271. tethrisextatetratediterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#6
  3272.  
  3273. tethriseptatetratediterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#7
  3274.  
  3275. tethrioctatetratediterstaculated-tethritertethrasquare =
  3276.  
  3277. E100(#^^##)^^#>#^^#>#^^#8
  3278.  
  3279. tethrinonatetratediterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#9
  3280.  
  3281. tethridecatetratediterstaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#10
  3282.  
  3283. ...
  3284.  
  3285. duturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#100
  3286.  
  3287. troiturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^#>#^^#>#^^#100
  3288.  
  3289. quatreturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##4
  3290.  
  3291. cinqturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##5
  3292.  
  3293. sesturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##6
  3294.  
  3295. septurreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##7
  3296.  
  3297. huiturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##8
  3298.  
  3299. neufturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##9
  3300.  
  3301. dexturreted-tethrastaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##10
  3302.  
  3303. ...
  3304.  
  3305. tethrasquarestaculated-tethritertethrasquare = E100(#^^##)^^#>#^^##100
  3306.  
  3307. terrible tethrasquarestaculated-tethritertethrasquare =E100((#^^##)^^#>#^^##)^^#100
  3308.  
  3309. terrible terrible tethrasquarestaculated-tethritertethrasquare =
  3310.  
  3311. E100(((#^^##)^^#>#^^##)^^#)^^#100
  3312.  
  3313. ...
  3314.  
  3315. hundred-ex-terrible tethrasquarestaculated-tethritertethrasquare =
  3316.  
  3317. E100(#^^##)^^#>(#^^##+#)100
  3318.  
  3319. ...
  3320.  
  3321. territethrasquarestaculated-tethritertethrasquare = E100(#^^##)^^#>(#^^##)^^#100
  3322.  
  3323. ... you may notice how long and technical the names are getting. They are starting to sound more like chemical formulas, or taxonomy than numbers. The reason for this is the same reason why chemical names and taxonomy are contain complicated names. When you start to have thousands of similar objects to name, you have to resort to longer names with interchangable parts to maintain clarity. xE^ allows for far greater freedom than previous ExE systems. There are many many many inbetween expressions between theobvious ones such as #^^##, #^^###, #^^#### etc. In fact we still have a long way to go to reach #^^###. We've only just begun with the ^^##-operator ...
  3324.  
  3325.  
  3326. duterritethrasquarestaculated-tethritertethrasquare =
  3327.  
  3328. E100(#^^##)^^#>((#^^##)^^#)^^#100
  3329.  
  3330.  
  3331.  
  3332.  
  3333. tethritertethrasquarestaculated-tethritertethrasquare =
  3334.  
  3335. E100(#^^##)^^#>(#^^##)^^#100
  3336.  
  3337. (also duturreted-tethritertethrasquare)
  3338.  
  3339.  
  3340.  
  3341.  
  3342. troisturreted-tethritertethrasquare
  3343.  
  3344. = E100(#^^##)^^#>(#^^##)^^#>(#^^##)^^#100
  3345.  
  3346. quatreturreted-tethritertethrasquare
  3347.  
  3348. = E100(#^^##)^^##4
  3349.  
  3350. cinqturreted-tethritertethrasquare
  3351.  
  3352. = E100(#^^##)^^##5
  3353.  
  3354. sesturreted-tethritertethrasquare
  3355.  
  3356. = E100(#^^##)^^##6
  3357.  
  3358. septurreted-tethritertethrasquare
  3359.  
  3360. = E100(#^^##)^^##7
  3361.  
  3362. huiturreted-tethritertethrasquare
  3363.  
  3364. = E100(#^^##)^^##8
  3365.  
  3366. neufturreted-tethritertethrasquare
  3367.  
  3368. = E100(#^^##)^^##9
  3369.  
  3370. dexturreted-tethritertethrasquare
  3371.  
  3372. = E100(#^^##)^^##10
  3373.  
  3374. ... and the nightmare continues ... and continues ... and continues ... and continues ...
  3375.  
  3376. secundotethrated-tethrasquare = E100(#^^##)^^##100
  3377.  
  3378. terrible secundotethrated-tethrasquare = E100((#^^##)^^##)^^#100
  3379.  
  3380. tethriterated-secundotethrated-tethrasquare = E100((#^^##)^^##)^^#>#100
  3381.  
  3382. duturreted-tethritersecundotethrated-tethrasquare
  3383.  
  3384. = E100((#^^##)^^#)^^#>((#^^##)^^#)^^#100
  3385.  
  3386. troisturreted-tethritersecundotethrated-tethrasquare
  3387.  
  3388. = E100((#^^##)^^##)^^##3
  3389.  
  3390. quatreturreted-tethritersecundotethrated-tethrasquare
  3391.  
  3392. = E100((#^^##)^^##)^^##4
  3393.  
  3394. cinqturreted-tethritersecundotethrated-tethrasquare
  3395.  
  3396. = E100((#^^##)^^##)^^##5
  3397.  
  3398. sesturreted-tethritersecundotethrated-tethrasquare
  3399.  
  3400. = E100((#^^##)^^##)^^##6
  3401.  
  3402. septurreted-tethritersecundotethrated-tethrasquare
  3403.  
  3404. = E100((#^^##)^^##)^^##7
  3405.  
  3406. huiturreted-tethritersecundotethrated-tethrasquare
  3407.  
  3408. = E100((#^^##)^^##)^^##8
  3409.  
  3410. neufturreted-tethritersecundotethrated-tethrasquare
  3411.  
  3412. = E100((#^^##)^^##)^^##9
  3413.  
  3414. dexturreted-tethritersecundotethrated-tethrasquare
  3415.  
  3416. = E100((#^^##)^^##)^^##10
  3417.  
  3418. ...
  3419.  
  3420. thrice-tethrasecunda = E100((#^^##)^^##)^^##100
  3421.  
  3422. quatrice-tethrasecunda = E100(((#^^##)^^##)^^##)^^##100
  3423.  
  3424. quincice-tethrasecunda = E100#^^##>#5
  3425.  
  3426. sextice-tethrasecunda = E100#^^##>#6
  3427.  
  3428. septice-tethrasecunda = E100#^^##>#7
  3429.  
  3430. octice-tethrasecunda = E100#^^##>#8
  3431.  
  3432. nonice-tethrasecunda = E100#^^##>#9
  3433.  
  3434. decice-tethrasecunda = E100#^^##>#10
  3435.  
  3436. ...
  3437.  
  3438. Tethrasquared-iterator Group
  3439.  
  3440.  
  3441. Here we reach a familiar form ...
  3442.  
  3443. tethrasquared-iterator = E100#^^##>#100
  3444.  
  3445. This is basically the same as a tethriterator, except that we are now iterating the 2nd tetrational operator, the tethrasecunda. With this in mind we can construct similar googolisms for the ^^##-operator, following the pattern of the iterated ^^#-operator...
  3446.  
  3447. tethrasquared-du-iterator = E100#^^##>(#+#)100
  3448.  
  3449. tethrasquared-triterator = E100#^^##>(#+#+#)100
  3450.  
  3451. tethrasquared-quaditerator = E100#^^##>(#+#+#+#)100
  3452.  
  3453. tethrasquared-quiditerator = E100#^^##>##5
  3454.  
  3455. tethrasquared-siditerator = E100#^^##>##6
  3456.  
  3457. tethrasquared-sepiterator = E100#^^##>##7
  3458.  
  3459. tethrasquared-ogditerator = E100#^^##>##8
  3460.  
  3461. tethrasquared-noniterator = E100#^^##>##9
  3462.  
  3463. tethrasquared-deciterator = E100#^^##>##10
  3464.  
  3465. ...
  3466.  
  3467. tethrasquared-griditerator = E100#^^##>##100
  3468.  
  3469. tethrasquared-cubiculator = E100#^^##>###100
  3470.  
  3471. tethrasquared-quarticulator = E100#^^##>####100
  3472.  
  3473. tethrasquared-quinticulator = E100#^^##>#^#5
  3474.  
  3475. tethrasquared-sexticulator = E100#^^##>#^#6
  3476.  
  3477. tethrasquared-septiculator = E100#^^##>#^#7
  3478.  
  3479. tethrasquared-octiculator = E100#^^##>#^#8
  3480.  
  3481. tethrasquared-noniculator = E100#^^##>#^#9
  3482.  
  3483. tethrasquared-deciculator = E100#^^##>#^#10
  3484.  
  3485. ...
  3486.  
  3487. tethrasquared-spatialator = E100#^^##>#^#100
  3488.  
  3489. ... keep in mind we are now iterating the ^^##-operator using #^# diagonalization! So we are moving away from tethrasquare at an alarming rate. We still have further to go however to reach the first application of the ^^###-operator...
  3490.  
  3491. tethrasquared-superspatialator = E100#^^##>#^#^#100
  3492.  
  3493. tethrasquared-quadratetratediterator = E100#^^##>#^#^#^#100
  3494.  
  3495. tethrasquared-quintatetratediterator = E100#^^##>#^^#5
  3496.  
  3497. tethrasquared-sextatetratediterator = E100#^^##>#^^#6
  3498.  
  3499. tethrasquared-septatetratediterator = E100#^^##>#^^#7
  3500.  
  3501. tethrasquared-octatetratediterator = E100#^^##>#^^#8
  3502.  
  3503. tethrasquared-nonatetratediterator = E100#^^##>#^^#9
  3504.  
  3505. tethrasquared-decatetratediterator = E100#^^##>#^^#10
  3506.  
  3507. ...
  3508.  
  3509. tethraturreted-tethrasquare = E100#^^##>#^^#100
  3510.  
  3511. duturretetethraturreted-tethrasquare = E100#^^##>#^^#>#^^#100
  3512.  
  3513. troisturretetethraturreted-tethrasquare = E100#^^##>#^^#>#^^#>#^^#100
  3514.  
  3515. quatreturretetethraturreted-tethrasquare = E100#^^##>#^^##4
  3516.  
  3517. cinqturretetethraturreted-tethrasquare = E100#^^##>#^^##5
  3518.  
  3519. sesturretetethraturreted-tethrasquare = E100#^^##>#^^##6
  3520.  
  3521. septurretetethraturreted-tethrasquare = E100#^^##>#^^##7
  3522.  
  3523. huiturretetethraturreted-tethrasquare = E100#^^##>#^^##8
  3524.  
  3525. neufturretetethraturreted-tethrasquare = E100#^^##>#^^##9
  3526.  
  3527. dexturretetethraturreted-tethrasquare = E100#^^##>#^^##10
  3528.  
  3529. ...
  3530.  
  3531. duturreted-tethrasquare = E100#^^##>#^^##100
  3532.  
  3533. terrible duturreted-tethrasquare = E100(#^^##>#^^##)^^#100
  3534.  
  3535. tethriterated duturreted-tethrasquare = E100(#^^##>#^^##)^^#>#100
  3536.  
  3537. terrisecunded duturreted-tethrasquare = E100(#^^##>#^^##)^^##100
  3538.  
  3539. double terrisecunded duturreted-tethrasquare = E100((#^^##>#^^##)^^##)^^##100
  3540.  
  3541. ...
  3542.  
  3543. hundred-ex-terrisecunded duturreted-tethrasquare = E100#^^##>(#^^##+#)100
  3544.  
  3545. ...
  3546.  
  3547. troisturreted-tethrasquare = E100#^^##>#^^##>#^^##100
  3548.  
  3549. quatreturreted-tethrasquare = E100#^^##>#^^##>#^^##>#^^##100
  3550.  
  3551. cinqturreted-tethrasquare = E100#^^###5
  3552.  
  3553. sesturreted-tethrasquare = E100#^^###6
  3554.  
  3555. septurreted-tethrasquare = E100#^^###7
  3556.  
  3557. huiturreted-tethrasquare = E100#^^###8
  3558.  
  3559. neufturreted-tethrasquare = E100#^^###9
  3560.  
  3561. dexturreted-tethrasquare = E100#^^###10
  3562.  
  3563. ...
  3564.  
  3565. Tethracubor Group
  3566.  
  3567.  
  3568.  
  3569.  
  3570.  
  3571.  
  3572. Now we're getting somewhere. We now introduce the third tetrational operator , ^^###. This operator is referred to by the roots tethratertia, tethracubor, or territertiated...
  3573.  
  3574.  
  3575.  
  3576.  
  3577.  
  3578. tethracubor = E100#^^###100
  3579.  
  3580. (also tethratertia)
  3581.  
  3582.  
  3583.  
  3584.  
  3585. ... once that is established there are plenty of constructions that follow, and some we can obtain with a little bit of tweaking ... here we go again ...
  3586.  
  3587.  
  3588.  
  3589.  
  3590. grand tethracubor = E100#^^###100#2
  3591.  
  3592.  
  3593.  
  3594.  
  3595. grangol-carta-tethracubor = E100#^^##100#100
  3596.  
  3597.  
  3598.  
  3599.  
  3600. godgahlah-carta-tethracubor = E100#^^##100#^#100
  3601.  
  3602.  
  3603.  
  3604.  
  3605. tethrathoth-carta-tethracubor = E100#^^##100#^^#100
  3606.  
  3607.  
  3608.  
  3609.  
  3610. tethrasquare-carta-tethracubor = E100#^^###100#^^##100
  3611.  
  3612.  
  3613.  
  3614.  
  3615. ...
  3616.  
  3617.  
  3618.  
  3619.  
  3620. duble-tethracubor = E100#^^###100#^^###100
  3621.  
  3622.  
  3623.  
  3624.  
  3625. treble-tethracubor = E100#^^###100#^^###100#^^###100
  3626.  
  3627.  
  3628.  
  3629.  
  3630. quadruble-tethracubor = E100#^^###*#5
  3631.  
  3632.  
  3633.  
  3634.  
  3635. quintuble-tethracubor = E100#^^###*#6
  3636.  
  3637.  
  3638.  
  3639.  
  3640. sextuble-tethracubor = E100#^^###*#7
  3641.  
  3642.  
  3643.  
  3644.  
  3645. septuble-tethracubor = E100#^^###*#8
  3646.  
  3647.  
  3648.  
  3649.  
  3650. octuble-tethracubor = E100#^^###*#9
  3651.  
  3652.  
  3653.  
  3654.  
  3655. nonuble-tethracubor = E100#^^###*#10
  3656.  
  3657.  
  3658.  
  3659.  
  3660. ...
  3661.  
  3662.  
  3663.  
  3664.  
  3665. centuble-tethracubor = E100#^^###*#100
  3666.  
  3667.  
  3668.  
  3669.  
  3670. ...
  3671.  
  3672.  
  3673.  
  3674.  
  3675. deutero-tethracubor = E100#^^###*#^^###100
  3676.  
  3677.  
  3678.  
  3679.  
  3680. trito-tethracubor = E100#^^###*#^^###*#^^###100
  3681.  
  3682.  
  3683.  
  3684.  
  3685. teterto-tethracubor = E100#^^###*#^^###*#^^###*#^^###100
  3686.  
  3687.  
  3688.  
  3689.  
  3690. pepto-tethracubor = E100(#^^###)^#5
  3691.  
  3692.  
  3693.  
  3694.  
  3695. exto-tethracubor = E100(#^^###)^#6
  3696.  
  3697.  
  3698.  
  3699.  
  3700. epto-tethracubor = E100(#^^###)^#7
  3701.  
  3702.  
  3703.  
  3704.  
  3705. ogdo-tethracubor = E100(#^^###)^#8
  3706.  
  3707.  
  3708.  
  3709.  
  3710. ento-tethracubor = E100(#^^###)^#9
  3711.  
  3712.  
  3713.  
  3714.  
  3715. dekato-tethracubor = E100(#^^###)^#10
  3716.  
  3717.  
  3718.  
  3719.  
  3720. ...
  3721.  
  3722.  
  3723.  
  3724.  
  3725. isosto-tethracubor = E100(#^^###)^#20
  3726.  
  3727.  
  3728.  
  3729.  
  3730. ...
  3731.  
  3732.  
  3733.  
  3734.  
  3735. hecato-tethracubor = E100(#^^###)^#100
  3736.  
  3737.  
  3738.  
  3739.  
  3740. here are some less immediate ones we can get with a little bit of modification from earlier googolism's ...
  3741.  
  3742.  
  3743.  
  3744.  
  3745.  
  3746. catenatethracubor = E100(#^^###)^#100
  3747.  
  3748.  
  3749.  
  3750.  
  3751. tethracuborgridulus = E100(#^^###)^##100
  3752.  
  3753.  
  3754.  
  3755.  
  3756. tethracuborcubiculus = E100(#^^###)^###100
  3757.  
  3758.  
  3759.  
  3760.  
  3761. tethracuborquarticulus = E100(#^^###)^####100
  3762.  
  3763.  
  3764.  
  3765.  
  3766. tethracuborquinticulus = E100(#^^###)^#^#5
  3767.  
  3768.  
  3769.  
  3770.  
  3771. tethracuborsexticulus = E100(#^^###)^#^#6
  3772.  
  3773.  
  3774.  
  3775.  
  3776. tethracuborsepticulus = E100(#^^###)^#^#7
  3777.  
  3778.  
  3779.  
  3780.  
  3781. tethracuborocticulus = E100(#^^###)^#^#8
  3782.  
  3783.  
  3784.  
  3785.  
  3786. tethracubornoniculus = E100(#^^###)^#^#9
  3787.  
  3788.  
  3789.  
  3790.  
  3791. tethracubordeciculus = E100(#^^###)^#^#10
  3792.  
  3793.  
  3794.  
  3795.  
  3796. ...
  3797.  
  3798.  
  3799.  
  3800.  
  3801. tethracuborgodgathored = E100(#^^###)^#^#100
  3802.  
  3803.  
  3804.  
  3805.  
  3806. tethracuborgralgathored = E100(#^^###)^#^##100
  3807.  
  3808.  
  3809.  
  3810.  
  3811. ...
  3812.  
  3813.  
  3814.  
  3815.  
  3816. tethracuborgodtotholed = E100(#^^###)^#^#^#100
  3817.  
  3818.  
  3819.  
  3820.  
  3821. ... here I'll introduce a new root operator. The virtua-operator takes the expression on the left and raises it to the power of the right (virtua is latin for power)...
  3822.  
  3823.  
  3824.  
  3825.  
  3826. tethracubor-virtua-tethrathoth = E100(#^^###)^#^^#100
  3827.  
  3828.  
  3829.  
  3830.  
  3831. tethracubor-virtua-tethriterator = E100(#^^###)^#^^#>#100
  3832.  
  3833.  
  3834.  
  3835.  
  3836. tethracubor-virtua-tethrasquare = E100(#^^###)^#^^##100
  3837.  
  3838.  
  3839.  
  3840.  
  3841. tethracubor-virtua-tethrasquared-iterator = E100(#^^###)^#^^##>#100
  3842.  
  3843.  
  3844.  
  3845.  
  3846. tethracubor-virtua-tethracubor = E100(#^^###)^(#^^###)100
  3847.  
  3848.  
  3849.  
  3850.  
  3851. ... we'll also want to be able to tetrate hyperials ...
  3852.  
  3853.  
  3854.  
  3855.  
  3856. tethracubor-deuterotetrated = E100(#^^###)^(#^^###)100
  3857.  
  3858.  
  3859.  
  3860.  
  3861. tethracubor-tritotetrated = E100(#^^###)^(#^^###)^(#^^###)100
  3862.  
  3863.  
  3864.  
  3865.  
  3866. tethracubor-tetertotetrated = E100(#^^###)^^#4
  3867.  
  3868.  
  3869.  
  3870.  
  3871. tethracubor-peptotetrated = E100(#^^###)^^#5
  3872.  
  3873.  
  3874.  
  3875.  
  3876. tethracubor-extotetrated = E100(#^^###)^^#6
  3877.  
  3878.  
  3879.  
  3880.  
  3881. tethracubor-eptotetrated = E100(#^^###)^^#7
  3882.  
  3883.  
  3884.  
  3885.  
  3886. tethracubor-ogdotetrated = E100(#^^###)^^#8
  3887.  
  3888.  
  3889.  
  3890.  
  3891. tethracubor-entotetrated = E100(#^^###)^^#9
  3892.  
  3893.  
  3894.  
  3895.  
  3896. tethracubor-dekatotetrated = E100(#^^###)^^#10
  3897.  
  3898.  
  3899.  
  3900.  
  3901. ...
  3902.  
  3903.  
  3904.  
  3905.  
  3906. tethracubor-isostotetrated = E100(#^^###)^^#20
  3907.  
  3908.  
  3909.  
  3910.  
  3911. ...
  3912.  
  3913.  
  3914.  
  3915.  
  3916. terrible tethracubor = E100(#^^###)^^#100
  3917.  
  3918.  
  3919.  
  3920.  
  3921. terrible terrible tethracubor = E100((#^^###)^^#)^^#100
  3922.  
  3923.  
  3924.  
  3925.  
  3926. hundred-ex-terrible tethracubor = E100(#^^###)^^#>#100
  3927.  
  3928.  
  3929.  
  3930.  
  3931. ... some further diagonalizations ...
  3932.  
  3933.  
  3934.  
  3935.  
  3936. tethritertethracubor = E100(#^^###)^^#>#100
  3937.  
  3938.  
  3939.  
  3940.  
  3941. duturreted-territethracubor = E100(#^^###)^^#>(#^^###)^^#100
  3942.  
  3943.  
  3944.  
  3945.  
  3946. triturreted-territethracubor = E100(#^^###)^^#>(#^^###)^^#>(#^^###)^^#100
  3947.  
  3948.  
  3949.  
  3950.  
  3951. tetraturreted-territethracubor = E100(#^^###)^^##4
  3952.  
  3953.  
  3954.  
  3955.  
  3956. penturreted-territethracubor = E100(#^^###)^^##5
  3957.  
  3958.  
  3959.  
  3960.  
  3961. hexturreted-territethracubor = E100(#^^###)^^##6
  3962.  
  3963.  
  3964.  
  3965.  
  3966. hepturreted-territethracubor = E100(#^^###)^^##7
  3967.  
  3968.  
  3969.  
  3970.  
  3971. ogturreted-territethracubor = E100(#^^###)^^##8
  3972.  
  3973.  
  3974.  
  3975.  
  3976. enturreted-territethracubor = E100(#^^###)^^##9
  3977.  
  3978.  
  3979.  
  3980.  
  3981. dekturreted-territethracubor = E100(#^^###)^^##10
  3982.  
  3983.  
  3984.  
  3985.  
  3986. ...
  3987.  
  3988.  
  3989.  
  3990.  
  3991. isosturreted-territethracubor = E100(#^^###)^^##20
  3992.  
  3993.  
  3994.  
  3995.  
  3996. ...
  3997.  
  3998.  
  3999.  
  4000.  
  4001. hecturreted-territethracubor = E100(#^^###)^^##100
  4002.  
  4003.  
  4004.  
  4005.  
  4006. ... on a higher diagonalization ...
  4007.  
  4008.  
  4009.  
  4010.  
  4011. terrisquared-tethracubor = E100(#^^###)^^##100
  4012.  
  4013.  
  4014.  
  4015.  
  4016. terrible terrisquared-tethracubor = E100((#^^###)^^##)^^#100
  4017.  
  4018.  
  4019.  
  4020.  
  4021. ...
  4022.  
  4023.  
  4024.  
  4025.  
  4026. territerated terrisquared-tethracubor = E100((#^^###)^^##)^^#>#100
  4027.  
  4028.  
  4029.  
  4030.  
  4031. double-terrisquared-tethracubor = E100((#^^###)^^##)^^##100
  4032.  
  4033.  
  4034.  
  4035.  
  4036. triple-terrisquared-tethracubor = E100(((#^^###)^^##)^^##)^^##100
  4037.  
  4038.  
  4039.  
  4040.  
  4041. quadruple-terrisquared-tethracubor = E100(#^^###)^^##>#4
  4042.  
  4043.  
  4044.  
  4045.  
  4046. quintuple-terrisquared-tethracubor = E100(#^^###)^^##>#5
  4047.  
  4048.  
  4049.  
  4050.  
  4051. sextuple-terrisquared-tethracubor = E100(#^^###)^^##>#6
  4052.  
  4053.  
  4054.  
  4055.  
  4056. septuple-terrisquared-tethracubor = E100(#^^###)^^##>#7
  4057.  
  4058.  
  4059.  
  4060.  
  4061. octuple-terrisquared-tethracubor = E100(#^^###)^^##>#8
  4062.  
  4063.  
  4064.  
  4065.  
  4066. nonuple-terrisquared-tethracubor = E100(#^^###)^^##>#9
  4067.  
  4068.  
  4069.  
  4070.  
  4071. decuple-terrisquared-tethracubor = E100(#^^###)^^##>#10
  4072.  
  4073.  
  4074.  
  4075.  
  4076. ...
  4077.  
  4078.  
  4079.  
  4080.  
  4081. vigintuple-terrisquared-tethracubor = E100(#^^###)^^##>#20
  4082.  
  4083.  
  4084.  
  4085.  
  4086. ...
  4087.  
  4088.  
  4089.  
  4090.  
  4091. centuple-terrisquared-tethracubor = E100(#^^###)^^##>#100
  4092.  
  4093.  
  4094.  
  4095.  
  4096. ... on a higher diagonalization ...
  4097.  
  4098.  
  4099.  
  4100.  
  4101. terrisquarediter-tethracubor = E100(#^^###)^^##>#100
  4102.  
  4103.  
  4104.  
  4105.  
  4106. ...
  4107.  
  4108.  
  4109.  
  4110.  
  4111. duturreted-terrisquared-tethracubor = E100(#^^###)^^##>(#^^###)^^##100
  4112.  
  4113.  
  4114.  
  4115.  
  4116. triturreted-terrisquared-tethracubor = E100(#^^###)^^###3
  4117.  
  4118.  
  4119.  
  4120.  
  4121. tetraturreted-terrisquared-tethracubor = E100(#^^###)^^###4
  4122.  
  4123.  
  4124.  
  4125.  
  4126. penturreted-terrisquared-tethracubor = E100(#^^###)^^###5
  4127.  
  4128.  
  4129.  
  4130.  
  4131. hexturreted-terrisquared-tethracubor = E100(#^^###)^^###6
  4132.  
  4133.  
  4134.  
  4135.  
  4136. hepturreted-terrisquared-tethracubor = E100(#^^###)^^###7
  4137.  
  4138.  
  4139.  
  4140.  
  4141. ogturreted-terrisquared-tethracubor = E100(#^^###)^^###8
  4142.  
  4143.  
  4144.  
  4145.  
  4146. enturreted-terrisquared-tethracubor = E100(#^^###)^^###9
  4147.  
  4148.  
  4149.  
  4150.  
  4151. dekturreted-terrisquared-tethracubor = E100(#^^###)^^###10
  4152.  
  4153.  
  4154.  
  4155.  
  4156. ...
  4157.  
  4158.  
  4159.  
  4160.  
  4161. isosturreted-terrisquared-tethracubor = E100(#^^###)^^###20
  4162.  
  4163.  
  4164.  
  4165.  
  4166. ...
  4167.  
  4168.  
  4169.  
  4170.  
  4171. hecturreted-terrisquared-tethracubor = E100(#^^###)^^###100
  4172.  
  4173.  
  4174.  
  4175.  
  4176. ... next level ...
  4177.  
  4178.  
  4179.  
  4180.  
  4181. tethradoplicubor = E100(#^^###)^^###100
  4182.  
  4183.  
  4184.  
  4185.  
  4186. terrible tethradoplicubor = E100((#^^###)^^###)^^#100
  4187.  
  4188.  
  4189.  
  4190.  
  4191. terrisquared-tethradoplicubor = E100((#^^###)^^###)^^##100
  4192.  
  4193.  
  4194.  
  4195.  
  4196. ...
  4197.  
  4198.  
  4199.  
  4200.  
  4201. tethratroplicubor = E100((#^^###)^^###)^^###100
  4202.  
  4203.  
  4204.  
  4205.  
  4206. tethraquadroplicubor = E100(((#^^###)^^###)^^###)^^###100
  4207.  
  4208.  
  4209.  
  4210.  
  4211. tethraquintoplicubor = E100#^^###>#5
  4212.  
  4213.  
  4214.  
  4215.  
  4216. tethrasextoplicubor = E100#^^###>#6
  4217.  
  4218.  
  4219.  
  4220.  
  4221. tethraseptoplicubor = E100#^^###>#7
  4222.  
  4223.  
  4224.  
  4225.  
  4226. tethra-octoplicubor = E100#^^###>#8
  4227.  
  4228.  
  4229.  
  4230.  
  4231. tethranonoplicubor = E100#^^###>#9
  4232.  
  4233.  
  4234.  
  4235.  
  4236. tethradecoplicubor = E100#^^###>#10
  4237.  
  4238.  
  4239.  
  4240.  
  4241. ...
  4242.  
  4243.  
  4244.  
  4245.  
  4246. tethravigintoplicubor = E100#^^###>#20
  4247.  
  4248.  
  4249.  
  4250.  
  4251. ...
  4252.  
  4253.  
  4254.  
  4255.  
  4256. tethracentoplicubor = E100#^^###>#100
  4257.  
  4258.  
  4259.  
  4260.  
  4261. ... and on to the next level ...
  4262.  
  4263.  
  4264.  
  4265.  
  4266. tethra-itercubor = E100#^^###>#100
  4267.  
  4268.  
  4269.  
  4270.  
  4271. tethra-ditercubor = E100#^^###>(#+#)100
  4272.  
  4273.  
  4274.  
  4275.  
  4276. tethra-tritercubor = E100#^^###>(#+#+#)100
  4277.  
  4278.  
  4279.  
  4280.  
  4281. tethra-quaditercubor = E100#^^###>(#+#+#+#)100
  4282.  
  4283.  
  4284.  
  4285.  
  4286. tethra-quiditercubor = E100#^^###>##5
  4287.  
  4288.  
  4289.  
  4290.  
  4291. tethra-siditercubor = E100#^^###>##6
  4292.  
  4293.  
  4294.  
  4295.  
  4296. tethra-sepitercubor = E100#^^###>##7
  4297.  
  4298.  
  4299.  
  4300.  
  4301. tethra-ogditercubor = E100#^^###>##8
  4302.  
  4303.  
  4304.  
  4305.  
  4306. tethra-nonitercubor = E100#^^###>##9
  4307.  
  4308.  
  4309.  
  4310.  
  4311. tethra-decitercubor = E100#^^###>##10
  4312.  
  4313.  
  4314.  
  4315.  
  4316. ...
  4317.  
  4318.  
  4319.  
  4320.  
  4321. tethra-vigintitercubor = E100#^^###>##20
  4322.  
  4323.  
  4324.  
  4325.  
  4326. ...
  4327.  
  4328.  
  4329.  
  4330.  
  4331. tethra-centitercubor = E100#^^###>##100
  4332.  
  4333.  
  4334.  
  4335.  
  4336. ... on a higher level ...
  4337.  
  4338.  
  4339.  
  4340.  
  4341. tethra-griditercubor = E100#^^###>##100
  4342.  
  4343.  
  4344.  
  4345.  
  4346. tethra-cubiculated-cubor = E100#^^###>###100
  4347.  
  4348.  
  4349.  
  4350.  
  4351. tethra-quarticulated-cubor = E100#^^###>####100
  4352.  
  4353.  
  4354.  
  4355.  
  4356. tethra-quinticulated-cubor = E100#^^###>#^#5
  4357.  
  4358.  
  4359.  
  4360.  
  4361. tethra-sexticulated-cubor = E100#^^###>#^#6
  4362.  
  4363.  
  4364.  
  4365.  
  4366. tethra-septiculated-cubor = E100#^^###>#^#7
  4367.  
  4368.  
  4369.  
  4370.  
  4371. tethra-octiculated-cubor = E100#^^###>#^#8
  4372.  
  4373.  
  4374.  
  4375.  
  4376. tethra-noniculated-cubor = E100#^^###>#^#9
  4377.  
  4378.  
  4379.  
  4380.  
  4381. tethra-deciculated-cubor = E100#^^###>#^#10
  4382.  
  4383.  
  4384.  
  4385.  
  4386. ...
  4387.  
  4388.  
  4389.  
  4390.  
  4391. tethra-viginticulated-cubor = E100#^^###>#^#20
  4392.  
  4393.  
  4394.  
  4395.  
  4396. ...
  4397.  
  4398.  
  4399.  
  4400.  
  4401. tethra-centiculated-cubor = E100#^^###>#^#100
  4402.  
  4403.  
  4404.  
  4405.  
  4406. ... on yet another level ...
  4407.  
  4408.  
  4409.  
  4410.  
  4411. duturreted-tethracubor = E100#^^###>#^^###100
  4412.  
  4413.  
  4414.  
  4415.  
  4416. triturreted-tethracubor = E100#^^###>#^^###>#^^###100
  4417.  
  4418.  
  4419.  
  4420.  
  4421. tetraturreted-tethracubor = E100#^^###>#^^###>#^^###>#^^###100
  4422.  
  4423.  
  4424.  
  4425.  
  4426. penturreted-tethracubor = E100#^^####5
  4427.  
  4428.  
  4429.  
  4430.  
  4431. hexturreted-tethracubor = E100#^^####6
  4432.  
  4433.  
  4434.  
  4435.  
  4436. hepturreted-tethracubor = E100#^^####7
  4437.  
  4438.  
  4439.  
  4440.  
  4441. ogturreted-tethracubor = E100#^^####8
  4442.  
  4443.  
  4444.  
  4445.  
  4446. enturreted-tethracubor = E100#^^####9
  4447.  
  4448.  
  4449.  
  4450.  
  4451. dekturreted-tethracubor = E100#^^####10
  4452.  
  4453.  
  4454.  
  4455.  
  4456. ...
  4457.  
  4458.  
  4459.  
  4460.  
  4461. isosturreted-tethracubor = E100#^^####20
  4462.  
  4463.  
  4464.  
  4465.  
  4466. ...
  4467.  
  4468.  
  4469.  
  4470.  
  4471.  
  4472. Tethrachoronicor Group
  4473.  
  4474.  
  4475.  
  4476.  
  4477. A 4-dimensional figure is popularly referred to as a polychoron. The next number can be thought of as employing (in very loose terms mind you) a 4th dimensional power tower of hyperions. Namely it uses the delimiter #^^#4 which is equivalent to the notion of the ordinal w^^w4. From this I derive the came tethrachoronicor ...
  4478.  
  4479.  
  4480.  
  4481.  
  4482.  
  4483. tethrachoronicor = E100#^^####100
  4484.  
  4485.  
  4486.  
  4487.  
  4488. (from tetration + polychoron)
  4489.  
  4490.  
  4491.  
  4492.  
  4493. Of coarse we can derive a whole family of googolism's based on extending tethrachoronicor using all the previously established constructions. Here is just a sampling...
  4494.  
  4495.  
  4496.  
  4497.  
  4498.  
  4499. grand tethrachoronicor = E100#^^####100#2
  4500.  
  4501.  
  4502.  
  4503.  
  4504. ...
  4505.  
  4506.  
  4507.  
  4508.  
  4509. grangol-carta-tethrachoronicor = E100#^^####100#100
  4510.  
  4511.  
  4512.  
  4513.  
  4514. ...
  4515.  
  4516.  
  4517.  
  4518.  
  4519. tethrachronicor-doplus = E100#^^####100#^^####100
  4520.  
  4521.  
  4522.  
  4523.  
  4524. tethrachoronicor-triplus = E100#^^####100#^^####100#^^####100
  4525.  
  4526.  
  4527.  
  4528.  
  4529. tethrachoronicor-quadruplus = E100#^^####*#5
  4530.  
  4531.  
  4532.  
  4533.  
  4534. tethrachoronicor-quintuplus = E100#^^####*#6
  4535.  
  4536.  
  4537.  
  4538.  
  4539. tethrachoronicor-sextuplus = E100#^^####*#7
  4540.  
  4541.  
  4542.  
  4543.  
  4544. tethrachoronicor-septuplus = E100#^^####*#8
  4545.  
  4546.  
  4547.  
  4548.  
  4549. tethrachoronicor-octuplus = E100#^^####*#9
  4550.  
  4551.  
  4552.  
  4553.  
  4554. tethrachoronicor-nonuplus = E100#^^####*#10
  4555.  
  4556.  
  4557.  
  4558.  
  4559. tethrachoronicor-decuplus = E100#^^####*#11
  4560.  
  4561.  
  4562.  
  4563.  
  4564. ...
  4565.  
  4566.  
  4567.  
  4568.  
  4569. deutero-tethrachoronicor = E100#^^####*#^^####100
  4570.  
  4571.  
  4572.  
  4573.  
  4574. trito-tethrachoronicor = E100#^^####*#^^####*#^^####100
  4575.  
  4576.  
  4577.  
  4578.  
  4579. teterto-tethrachoronicor = E100(#^^####)^#4
  4580.  
  4581.  
  4582.  
  4583.  
  4584. pepto-tethrachoronicor = E100(#^^####)^#5
  4585.  
  4586.  
  4587.  
  4588.  
  4589. exto-tethrachoronicor = E100(#^^####)^#6
  4590.  
  4591.  
  4592.  
  4593.  
  4594. epto-tethrachoronicor = E100(#^^####)^#7
  4595.  
  4596.  
  4597.  
  4598.  
  4599. ogdo-tethrachoronicor = E100(#^^####)^#8
  4600.  
  4601.  
  4602.  
  4603.  
  4604. ento-tethrachoronicor = E100(#^^####)^#9
  4605.  
  4606.  
  4607.  
  4608.  
  4609. dekato-tethrachoronicor = E100(#^^####)^#10
  4610.  
  4611.  
  4612.  
  4613.  
  4614. ...
  4615.  
  4616.  
  4617.  
  4618.  
  4619. catenatethrachoronicor = E100(#^^####)^#100
  4620.  
  4621.  
  4622.  
  4623.  
  4624. tethrachoronigrid = E100(#^^####)^##100
  4625.  
  4626.  
  4627.  
  4628.  
  4629. tethrachoronicube = E100(#^^####)^###100
  4630.  
  4631.  
  4632.  
  4633.  
  4634. tethrachoronitessor = E100(#^^####)^####100
  4635.  
  4636.  
  4637.  
  4638.  
  4639. tethrachoronipentor = E100(#^^####)^#^#5
  4640.  
  4641.  
  4642.  
  4643.  
  4644. tethrachoronihexor = E100(#^^####)^#^#6
  4645.  
  4646.  
  4647.  
  4648.  
  4649. tethrachoroniheptor = E100(#^^####)^#^#7
  4650.  
  4651.  
  4652.  
  4653.  
  4654. tethrachoroni-octor = E100(#^^####)^#^#8
  4655.  
  4656.  
  4657.  
  4658.  
  4659. tethrachoroni-entor = E100(#^^####)^#^#9
  4660.  
  4661.  
  4662.  
  4663.  
  4664. tethrachoroni-dector = E100(#^^####)^#^#10
  4665.  
  4666.  
  4667.  
  4668.  
  4669. ...
  4670.  
  4671.  
  4672.  
  4673.  
  4674. deutetrated-tethrachoronicor = E100(#^^####)^(#^^####)100
  4675.  
  4676.  
  4677.  
  4678.  
  4679. tritetrated-tethrachoronicor = E100(#^^####)^(#^^####)^(#^^####)100
  4680.  
  4681.  
  4682.  
  4683.  
  4684. tetratetrated-tethrachoronicor = E100(#^^####)^^#4
  4685.  
  4686.  
  4687.  
  4688.  
  4689. pentatetrated-tethrachoronicor = E100(#^^####)^^#5
  4690.  
  4691.  
  4692.  
  4693.  
  4694. hexatetrated-tethrachoronicor = E100(#^^####)^^#6
  4695.  
  4696.  
  4697.  
  4698.  
  4699. heptatetrated-tethrachoronicor = E100(#^^####)^^#7
  4700.  
  4701.  
  4702.  
  4703.  
  4704. octatetrated-tethrachoronicor = E100(#^^####)^^#8
  4705.  
  4706.  
  4707.  
  4708.  
  4709. ennatetrated-tethrachoronicor = E100(#^^####)^^#9
  4710.  
  4711.  
  4712.  
  4713.  
  4714. dekatetrated-tethrachoronicor = E100(#^^####)^^#10
  4715.  
  4716.  
  4717.  
  4718.  
  4719. ...
  4720.  
  4721.  
  4722.  
  4723.  
  4724. terrible tethrachoronicor = E100(#^^####)^^#100
  4725.  
  4726.  
  4727.  
  4728.  
  4729. terrible terrible tethrachoronicor = E100((#^^####)^^#)^^#100
  4730.  
  4731.  
  4732.  
  4733.  
  4734. ...
  4735.  
  4736.  
  4737.  
  4738.  
  4739. territerated-tethrachoronicor = E100(#^^####)^^#>#100
  4740.  
  4741.  
  4742.  
  4743.  
  4744. terriditerated-tethrachoronicor = E100(#^^####)^^#>(#+#)100
  4745.  
  4746.  
  4747.  
  4748.  
  4749. territriterated-tethrachoronicor = E100(#^^####)^^#>(#+#+#)100
  4750.  
  4751.  
  4752.  
  4753.  
  4754. ...
  4755.  
  4756.  
  4757.  
  4758.  
  4759. duturreted-territethrachoronicor = E100(#^^####)^^#>(#^^####)^^#100
  4760.  
  4761.  
  4762.  
  4763.  
  4764. triturreted-territethrachoronicor = E100(#^^####)^^##3
  4765.  
  4766.  
  4767.  
  4768.  
  4769. tetraturreted-territethrachoronicor = E100(#^^####)^^##4
  4770.  
  4771.  
  4772.  
  4773.  
  4774. ...
  4775.  
  4776.  
  4777.  
  4778.  
  4779. terrisquared-tethrachoronicor = E100(#^^####)^^##100
  4780.  
  4781.  
  4782.  
  4783.  
  4784. terrible terrisquared-tethrachoronicor = E100((#^^####)^^##)^^#100
  4785.  
  4786.  
  4787.  
  4788.  
  4789. double terrisquared-tethrachoronicor = E100((#^^####)^^##)^^##100
  4790.  
  4791.  
  4792.  
  4793.  
  4794. terrible double terrisquared-tethrachoronicor = E100(((#^^####)^^##)^^##)^^#100
  4795.  
  4796.  
  4797.  
  4798.  
  4799. triple terrisquared-tethrachoronicor = E100(#^^####)^^##>#3
  4800.  
  4801.  
  4802.  
  4803.  
  4804. quadruple terrisquared-tethrachoronicor = E100(#^^####)^^##>#4
  4805.  
  4806.  
  4807.  
  4808.  
  4809. quintuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#5
  4810.  
  4811.  
  4812.  
  4813.  
  4814. sextuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#6
  4815.  
  4816.  
  4817.  
  4818.  
  4819. septuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#7
  4820.  
  4821.  
  4822.  
  4823.  
  4824. octuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#8
  4825.  
  4826.  
  4827.  
  4828.  
  4829. nonuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#9
  4830.  
  4831.  
  4832.  
  4833.  
  4834. decuple terrisquared-tethrachoronicor = E100(#^^####)^^##>#10
  4835.  
  4836.  
  4837.  
  4838.  
  4839. ...
  4840.  
  4841.  
  4842.  
  4843.  
  4844. duturreted-terrisquared-tethrachoronicor = E100(#^^####)^^##>(#^^####)^^##100
  4845.  
  4846.  
  4847.  
  4848.  
  4849. triturreted-terrisquared-tethrachoronicor = E100(#^^####)^^###3
  4850.  
  4851.  
  4852.  
  4853.  
  4854. tetraturreted-terrisquared-tethrachoronicor = E100(#^^####)^^###4
  4855.  
  4856.  
  4857.  
  4858.  
  4859. ...
  4860.  
  4861.  
  4862.  
  4863.  
  4864. terricubed-tethrachoronicor = E100(#^^####)^^###100
  4865.  
  4866.  
  4867.  
  4868.  
  4869. double terricubed-tethrachoronicor = E100((#^^####)^^###)^^###100
  4870.  
  4871.  
  4872.  
  4873.  
  4874. triple terricubed-tethrachoronicor = E100(#^^####)^^###>#3
  4875.  
  4876.  
  4877.  
  4878.  
  4879. ...
  4880.  
  4881.  
  4882.  
  4883.  
  4884. duturreted-terricubed-tethrachoronicor = E100(#^^####)^^###>(#^^####)^^###100
  4885.  
  4886.  
  4887.  
  4888.  
  4889. triturreted-terricubed-tethrachoronicor = E100(#^^####)^^####3
  4890.  
  4891.  
  4892.  
  4893.  
  4894. tetraturreted-terricubed-tethrachoronicor = E100(#^^####)^^####4
  4895.  
  4896.  
  4897.  
  4898.  
  4899. ...
  4900.  
  4901.  
  4902.  
  4903.  
  4904. tethra-deuterchoronicor = E100(#^^####)^^####100
  4905.  
  4906.  
  4907.  
  4908.  
  4909. tethra-tritochoronicor = E100((#^^####)^^####)^^####100
  4910.  
  4911.  
  4912.  
  4913.  
  4914. tethra-tetertochoronicor = E100#^^####>#4
  4915.  
  4916.  
  4917.  
  4918.  
  4919. tethra-peptochoronicor = E100#^^####>#5
  4920.  
  4921.  
  4922.  
  4923.  
  4924. tethra-extochoronicor = E100#^^####>#6
  4925.  
  4926.  
  4927.  
  4928.  
  4929. tethra-eptochoronicor = E100#^^####>#7
  4930.  
  4931.  
  4932.  
  4933.  
  4934. tethra-ogdochoronicor = E100#^^####>#8
  4935.  
  4936.  
  4937.  
  4938.  
  4939. tethra-entochoronicor = E100#^^####>#9
  4940.  
  4941.  
  4942.  
  4943.  
  4944. tethra-dekatochoronicor = E100#^^####>#10
  4945.  
  4946.  
  4947.  
  4948.  
  4949. ...
  4950.  
  4951.  
  4952.  
  4953.  
  4954. duturreted-tethrachoronicor = E100#^^####>#^^####100
  4955.  
  4956.  
  4957.  
  4958.  
  4959. triturreted-tethrachoronicor = E100#^^####>#^^####>#^^####100
  4960.  
  4961.  
  4962.  
  4963.  
  4964. tetraturreted-tetrhachoronicor = E100#^^#####4
  4965.  
  4966.  
  4967.  
  4968.  
  4969. ...
  4970.  
  4971.  
  4972.  
  4973.  
  4974.  
  4975. tethrateronicor group
  4976.  
  4977.  
  4978.  
  4979.  
  4980.  
  4981. ... as you can probably tell we have already settled into a regular pattern. I'll only give a smattering of googolism's possible for the next few groups. Keep in mind the pattern we've just established is still just the very beginning. We haven't even gotten to the pentational cases yet. We've still got a long way to go ...
  4982.  
  4983.  
  4984.  
  4985.  
  4986.  
  4987. tethrateronicor = E100#^^#^#5
  4988.  
  4989.  
  4990.  
  4991.  
  4992. (from tetration + polyteron )
  4993.  
  4994.  
  4995.  
  4996.  
  4997. note: for rest of examples, resolve fundamental sequences before proceeding
  4998.  
  4999.  
  5000.  
  5001.  
  5002. grand tethrateronicor = E100#^^#5100#2
  5003.  
  5004.  
  5005.  
  5006.  
  5007. ...
  5008.  
  5009.  
  5010.  
  5011.  
  5012. grangol-carta-tethrateronicor = E100#^^#5100#100
  5013.  
  5014.  
  5015.  
  5016.  
  5017. ...
  5018.  
  5019.  
  5020.  
  5021.  
  5022. tethrateronicor-doplus = E100#^^#5100#^^#5100
  5023.  
  5024.  
  5025.  
  5026.  
  5027. ...
  5028.  
  5029.  
  5030.  
  5031.  
  5032. deutero-tethrateronicor = E100#^^#5*#^^#5100
  5033.  
  5034.  
  5035.  
  5036.  
  5037. ...
  5038.  
  5039.  
  5040.  
  5041.  
  5042. catenatethrateronicor = E100(#^^#5)^#100
  5043.  
  5044.  
  5045.  
  5046.  
  5047. ...
  5048.  
  5049.  
  5050.  
  5051.  
  5052. deutetrated-tethrateronicor = E100(#^^#5)^(#^^#5)100
  5053.  
  5054.  
  5055.  
  5056.  
  5057. ...
  5058.  
  5059.  
  5060.  
  5061.  
  5062. terrible tethrateronicor = E100(#^^#5)^^#100
  5063.  
  5064.  
  5065.  
  5066.  
  5067. ...
  5068.  
  5069.  
  5070.  
  5071.  
  5072. territerated tethrateronicor = E100(#^^#5)^^#>#100
  5073.  
  5074.  
  5075.  
  5076.  
  5077. ...
  5078.  
  5079.  
  5080.  
  5081.  
  5082. duturreted-territethrateronicor = E100(#^^#5)^^#>(#^^#5)^^#100
  5083.  
  5084.  
  5085.  
  5086.  
  5087. ...
  5088.  
  5089.  
  5090.  
  5091.  
  5092. terrisquared-tethrateronicor = E100(#^^#5)^^##100
  5093.  
  5094.  
  5095.  
  5096.  
  5097. terricubed-tethrateronicor = E100(#^^#5)^^###100
  5098.  
  5099.  
  5100.  
  5101.  
  5102. territesserated-tethrateronicor = E100(#^^#5)^^####100
  5103.  
  5104.  
  5105.  
  5106.  
  5107. tethra-deuterteronicor = E100(#^^#5)^^#5100
  5108.  
  5109.  
  5110.  
  5111.  
  5112. ...
  5113.  
  5114.  
  5115.  
  5116.  
  5117. tethra-iterteronicor = E100#^^#5>#100
  5118.  
  5119.  
  5120.  
  5121.  
  5122. ...
  5123.  
  5124.  
  5125.  
  5126.  
  5127. duturreted-tethrateronicor = E100#^^#5>#^^#5100
  5128.  
  5129.  
  5130.  
  5131.  
  5132. triturreted-tethrateronicor = E100#^^#5>#^^#5>#^^#5100
  5133.  
  5134.  
  5135.  
  5136.  
  5137. tetraturreted-tethrateronicor = E100#^^#5>#^^#5>#^^#5>#^^#5100
  5138.  
  5139.  
  5140.  
  5141.  
  5142. ...
  5143.  
  5144.  
  5145.  
  5146.  
  5147.  
  5148. tethrapetonicor group
  5149.  
  5150.  
  5151.  
  5152.  
  5153.  
  5154. tethrapetonicor = E100#^^#^#6
  5155.  
  5156.  
  5157.  
  5158.  
  5159.  
  5160. (from tetration + polypeton )
  5161.  
  5162.  
  5163.  
  5164.  
  5165. grand tethrapetonicor = E100#^^#^(6)100#2
  5166.  
  5167.  
  5168.  
  5169.  
  5170. ...
  5171.  
  5172.  
  5173.  
  5174.  
  5175. grangol-carta-tethrapetonicor = E100#^^#^(6)100#100
  5176.  
  5177.  
  5178.  
  5179.  
  5180. ...
  5181.  
  5182.  
  5183.  
  5184.  
  5185. tethrapetonicor-doplus = E100#^^#^(6)100#^^#^(6)100
  5186.  
  5187.  
  5188.  
  5189.  
  5190. ...
  5191.  
  5192.  
  5193.  
  5194.  
  5195. deutero-tethrapetonicor = E100#^^#^(6)*#^^#^(6)100
  5196.  
  5197.  
  5198.  
  5199.  
  5200. ...
  5201.  
  5202.  
  5203.  
  5204.  
  5205. catenatethrapetonicor = E100(#^^#^(6))^#100
  5206.  
  5207.  
  5208.  
  5209.  
  5210. ...
  5211.  
  5212.  
  5213.  
  5214.  
  5215. deutetrated-tethrapetonicor = E100(#^^#^(6))^(#^^#^(6))100
  5216.  
  5217.  
  5218.  
  5219.  
  5220. ...
  5221.  
  5222.  
  5223.  
  5224.  
  5225. terrible tethrapetonicor = E100(#^^#^(6))^^#100
  5226.  
  5227.  
  5228.  
  5229.  
  5230. ...
  5231.  
  5232.  
  5233.  
  5234.  
  5235. territerated tethrapetonicor = E100(#^^#^(6))^^#>#100
  5236.  
  5237.  
  5238.  
  5239.  
  5240. ...
  5241.  
  5242.  
  5243.  
  5244.  
  5245. duturreted-territethrapetonicor = E100(#^^#^(6))^^#>(#^^#^(6))^^#100
  5246.  
  5247.  
  5248.  
  5249.  
  5250. ...
  5251.  
  5252.  
  5253.  
  5254.  
  5255. terrisquared-tethrapetonicor = E100(#^^#^(6))^^##100
  5256.  
  5257.  
  5258.  
  5259.  
  5260. terricubed-tethrapetonicor = E100(#^^#^(6))^^###100
  5261.  
  5262.  
  5263.  
  5264.  
  5265. territesserated-tethrapetonicor = E100(#^^#^(6))^^####100
  5266.  
  5267.  
  5268.  
  5269.  
  5270. terripenterated-tethrapetonicor = E100(#^^#^(6))^^#^(5)100
  5271.  
  5272.  
  5273.  
  5274.  
  5275. tethra-deuterpetonicor = E100(#^^#^(6))^^#^(6)100
  5276.  
  5277.  
  5278.  
  5279.  
  5280. ...
  5281.  
  5282.  
  5283.  
  5284.  
  5285. tethra-iterpetonicor = E100#^^#^(6)>#100
  5286.  
  5287.  
  5288.  
  5289.  
  5290. ...
  5291.  
  5292.  
  5293.  
  5294.  
  5295. duturreted-tethrapetonicor = E100#^^#^(6)>#^^#^(6)100
  5296.  
  5297.  
  5298.  
  5299.  
  5300. triturreted-tethrapetonicor = E100#^^#^(6)>#^^#^(6)>#^^#^(6)100
  5301.  
  5302.  
  5303.  
  5304.  
  5305. tetraturreted-tethrapetonicor = E100#^^#^(6)>#^^#^(6)>#^^#^(6)>#^^#^(6)100
  5306.  
  5307.  
  5308.  
  5309.  
  5310. ...
  5311.  
  5312.  
  5313.  
  5314.  
  5315.  
  5316. tethrahexonicor group
  5317.  
  5318.  
  5319.  
  5320.  
  5321.  
  5322. tethrahexonicor = E100#^^#^#7
  5323.  
  5324.  
  5325.  
  5326.  
  5327. (from tetration + polyecton )
  5328.  
  5329.  
  5330.  
  5331.  
  5332.  
  5333. grand tethrahexonicor = E100#^^#^(7)100#2
  5334.  
  5335.  
  5336.  
  5337.  
  5338. ...
  5339.  
  5340.  
  5341.  
  5342.  
  5343. grangol-carta-tethrahexonicor = E100#^^#^(7)100#100
  5344.  
  5345.  
  5346.  
  5347.  
  5348. ...
  5349.  
  5350.  
  5351.  
  5352.  
  5353. tethrahexonicor-doplus = E100#^^#^(7)100#^^#^(7)100
  5354.  
  5355.  
  5356.  
  5357.  
  5358. ...
  5359.  
  5360.  
  5361.  
  5362.  
  5363. deutero-tethrahexonicor = E100#^^#^(7)*#^^#^(7)100
  5364.  
  5365.  
  5366.  
  5367.  
  5368. ...
  5369.  
  5370.  
  5371.  
  5372.  
  5373. tethrahexonichain = E100(#^^#^(7))^#100
  5374.  
  5375.  
  5376.  
  5377.  
  5378. ...
  5379.  
  5380.  
  5381.  
  5382.  
  5383. deutetrated-tethrahexonicor = E100(#^^#^(7))^(#^^#^(7))100
  5384.  
  5385.  
  5386.  
  5387.  
  5388. ...
  5389.  
  5390.  
  5391.  
  5392.  
  5393. terrible tethrahexonicor = E100(#^^#^(7))^^#100
  5394.  
  5395.  
  5396.  
  5397.  
  5398. ...
  5399.  
  5400.  
  5401.  
  5402.  
  5403. territerated tethrahexonicor = E100(#^^#^(7))^^#>#100
  5404.  
  5405.  
  5406.  
  5407.  
  5408. ...
  5409.  
  5410.  
  5411.  
  5412.  
  5413. duturreted-territethrahexonicor = E100(#^^#^(7))^^#>(#^^#^(7))^^#100
  5414.  
  5415.  
  5416.  
  5417.  
  5418. ...
  5419.  
  5420.  
  5421.  
  5422.  
  5423. terrisquared-tethrahexonicor = E100(#^^#^(7))^^##100
  5424.  
  5425.  
  5426.  
  5427.  
  5428. terricubed-tethrahexonicor = E100(#^^#^(7))^^###100
  5429.  
  5430.  
  5431.  
  5432.  
  5433. territesserated-tethrahexonicor = E100(#^^#^(7))^^####100
  5434.  
  5435.  
  5436.  
  5437.  
  5438. terripenterated-tethrahexonicor = E100(#^^#^(7))^^#^(5)100
  5439.  
  5440.  
  5441.  
  5442.  
  5443. terrihexerated-tethrahexonicor = E100(#^^#^(7))^^#^(6)100
  5444.  
  5445.  
  5446.  
  5447.  
  5448. tethra-deuterhexonicor = E100(#^^#^(7))^^#^(7)100
  5449.  
  5450.  
  5451.  
  5452.  
  5453. ...
  5454.  
  5455.  
  5456.  
  5457.  
  5458. tethra-iterhexonicor = E100#^^#^(7)>#100
  5459.  
  5460.  
  5461.  
  5462.  
  5463. ...
  5464.  
  5465.  
  5466.  
  5467.  
  5468. duturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)100
  5469.  
  5470.  
  5471.  
  5472.  
  5473. triturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)100
  5474.  
  5475.  
  5476.  
  5477.  
  5478. tetraturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)>#^^#^(7)100
  5479.  
  5480.  
  5481.  
  5482.  
  5483. ...
  5484.  
  5485.  
  5486.  
  5487.  
  5488.  
  5489. tethraheptonicor group
  5490.  
  5491.  
  5492.  
  5493.  
  5494.  
  5495. tethraheptonicor = E100#^^#^#8
  5496.  
  5497.  
  5498.  
  5499.  
  5500.  
  5501. (from tetration + polyzetton )
  5502.  
  5503.  
  5504.  
  5505.  
  5506.  
  5507. grand tethraheptonicor = E100#^^#^(8)100#2
  5508.  
  5509.  
  5510.  
  5511.  
  5512. ...
  5513.  
  5514.  
  5515.  
  5516.  
  5517. grangol-carta-tethraheptonicor = E100#^^#^(8)100#100
  5518.  
  5519.  
  5520.  
  5521.  
  5522. ...
  5523.  
  5524.  
  5525.  
  5526.  
  5527. tethraheptonicor-doplus = E100#^^#^(8)100#^^#^(8)100
  5528.  
  5529.  
  5530.  
  5531.  
  5532. ...
  5533.  
  5534.  
  5535.  
  5536.  
  5537. deutero-tethraheptonicor = E100#^^#^(8)*#^^#^(8)100
  5538.  
  5539.  
  5540.  
  5541.  
  5542. ...
  5543.  
  5544.  
  5545.  
  5546.  
  5547. tethraheptonifact = E100(#^^#^(8))^#100
  5548.  
  5549.  
  5550.  
  5551.  
  5552. ...
  5553.  
  5554.  
  5555.  
  5556.  
  5557. deutetrated-tethraheptonicor = E100(#^^#^(8))^(#^^#^(8))100
  5558.  
  5559.  
  5560.  
  5561.  
  5562. ...
  5563.  
  5564.  
  5565.  
  5566.  
  5567. terrible tethraheptonicor = E100(#^^#^(8))^^#100
  5568.  
  5569.  
  5570.  
  5571.  
  5572. ...
  5573.  
  5574.  
  5575.  
  5576.  
  5577. territerated tethraheptonicor = E100(#^^#^(8))^^#>#100
  5578.  
  5579.  
  5580.  
  5581.  
  5582. ...
  5583.  
  5584.  
  5585.  
  5586.  
  5587. duturreted-territethraheptonicor = E100(#^^#^(8))^^#>(#^^#^(8))^^#100
  5588.  
  5589.  
  5590.  
  5591.  
  5592. ...
  5593.  
  5594.  
  5595.  
  5596.  
  5597. terrisquared-tethraheptonicor = E100(#^^#^(8))^^##100
  5598.  
  5599.  
  5600.  
  5601.  
  5602. terricubed-tethraheptonicor= E100(#^^#^(8))^^###100
  5603.  
  5604.  
  5605.  
  5606.  
  5607. territesserated-tethraheptonicor = E100(#^^#^(8))^^####100
  5608.  
  5609.  
  5610.  
  5611.  
  5612. terripenterated-tethraheptonicor = E100(#^^#^(8))^^#^(5)100
  5613.  
  5614.  
  5615.  
  5616.  
  5617. terrihexerated-tethraheptonicor = E100(#^^#^(8))^^#^(6)100
  5618.  
  5619.  
  5620.  
  5621.  
  5622. terrihepterated-tethraheptonicor = E100(#^^#^(8))^^#^(7)100
  5623.  
  5624.  
  5625.  
  5626.  
  5627. tethra-deuterheptonicor = E100(#^^#^(8))^^#^(8)100
  5628.  
  5629.  
  5630.  
  5631.  
  5632. ...
  5633.  
  5634.  
  5635.  
  5636.  
  5637. tethra-iterheptonicor = E100#^^#^(8)>#100
  5638.  
  5639.  
  5640.  
  5641.  
  5642. ...
  5643.  
  5644.  
  5645.  
  5646.  
  5647. duturreted-tethraheptonicor = E100#^^#^(8)>#^^#^(8)100
  5648.  
  5649.  
  5650.  
  5651.  
  5652. triturreted-tethraheptonicor = E100#^^#^(8)>#^^#^(8)>#^^#^(8)100
  5653.  
  5654.  
  5655.  
  5656.  
  5657. tetraturreted-tethraheptonicor = E100#^^#^(8)>#^^#^(8)>#^^#^(8)>#^^#^(8)100
  5658.  
  5659.  
  5660.  
  5661.  
  5662. ...
  5663.  
  5664.  
  5665.  
  5666.  
  5667.  
  5668.  
  5669. tethra-ogdonicor group
  5670.  
  5671.  
  5672. #############################################################
  5673. ###########################################################
  5674.  
  5675. tethra-ogdonicor = E100#^^#^#9
  5676.  
  5677.  
  5678.  
  5679.  
  5680.  
  5681. tethrahexonicor = E100#^^#^#7
  5682.  
  5683.  
  5684.  
  5685.  
  5686. (from tetration + polyecton )
  5687.  
  5688.  
  5689.  
  5690.  
  5691.  
  5692. grand tethrahexonicor = E100#^^#^(7)100#2
  5693.  
  5694.  
  5695.  
  5696.  
  5697. ...
  5698.  
  5699.  
  5700.  
  5701.  
  5702. grangol-carta-tethrahexonicor = E100#^^#^(7)100#100
  5703.  
  5704.  
  5705.  
  5706.  
  5707. ...
  5708.  
  5709.  
  5710.  
  5711.  
  5712. tethrahexonicor-doplus = E100#^^#^(7)100#^^#^(7)100
  5713.  
  5714.  
  5715.  
  5716.  
  5717. ...
  5718.  
  5719.  
  5720.  
  5721.  
  5722. deutero-tethrahexonicor = E100#^^#^(7)*#^^#^(7)100
  5723.  
  5724.  
  5725.  
  5726.  
  5727. ...
  5728.  
  5729.  
  5730.  
  5731.  
  5732. tethrahexonifact = E100(#^^#^(7))^#100
  5733.  
  5734.  
  5735.  
  5736.  
  5737. ...
  5738.  
  5739.  
  5740.  
  5741.  
  5742. deutetrated-tethrahexonicor = E100(#^^#^(7))^(#^^#^(7))100
  5743.  
  5744.  
  5745.  
  5746.  
  5747. ...
  5748.  
  5749.  
  5750.  
  5751.  
  5752. terrible tethrahexonicor = E100(#^^#^(7))^^#100
  5753.  
  5754.  
  5755.  
  5756.  
  5757. ...
  5758.  
  5759.  
  5760.  
  5761.  
  5762. territerated tethrahexonicor = E100(#^^#^(7))^^#>#100
  5763.  
  5764.  
  5765.  
  5766.  
  5767. ...
  5768.  
  5769.  
  5770.  
  5771.  
  5772. duturreted-territethrahexonicor = E100(#^^#^(7))^^#>(#^^#^(7))^^#100
  5773.  
  5774.  
  5775.  
  5776.  
  5777. ...
  5778.  
  5779.  
  5780.  
  5781.  
  5782. terrisquared-tethrahexonicor = E100(#^^#^(7))^^##100
  5783.  
  5784.  
  5785.  
  5786.  
  5787. terricubed-tethrahexonicor = E100(#^^#^(7))^^###100
  5788.  
  5789.  
  5790.  
  5791.  
  5792. territesserated-tethrahexonicor = E100(#^^#^(7))^^####100
  5793.  
  5794.  
  5795.  
  5796.  
  5797. terripenterated-tethrahexonicor = E100(#^^#^(7))^^#^(5)100
  5798.  
  5799.  
  5800.  
  5801.  
  5802. terrihexerated-tethrahexonicor = E100(#^^#^(7))^^#^(6)100
  5803.  
  5804.  
  5805.  
  5806.  
  5807. tethra-deuterhexonicor = E100(#^^#^(7))^^#^(7)100
  5808.  
  5809.  
  5810.  
  5811.  
  5812. ...
  5813.  
  5814.  
  5815.  
  5816.  
  5817. tethra-iterhexonicor = E100#^^#^(7)>#100
  5818.  
  5819.  
  5820.  
  5821.  
  5822. ...
  5823.  
  5824.  
  5825.  
  5826.  
  5827. duturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)100
  5828.  
  5829.  
  5830.  
  5831.  
  5832. triturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)100
  5833.  
  5834.  
  5835.  
  5836.  
  5837. tetraturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)>#^^#^(7)100
  5838.  
  5839.  
  5840.  
  5841.  
  5842. ...
  5843.  
  5844.  
  5845.  
  5846.  
  5847.  
  5848.  
  5849.  
  5850.  
  5851.  
  5852. tethra-ennonicor = E100#^^#^#10
  5853.  
  5854.  
  5855.  
  5856.  
  5857.  
  5858. tethrahexonicor = E100#^^#^#7
  5859.  
  5860.  
  5861.  
  5862.  
  5863. (from tetration + polyecton )
  5864.  
  5865.  
  5866.  
  5867.  
  5868.  
  5869. grand tethrahexonicor = E100#^^#^(7)100#2
  5870.  
  5871.  
  5872.  
  5873.  
  5874. ...
  5875.  
  5876.  
  5877.  
  5878.  
  5879. grangol-carta-tethrahexonicor = E100#^^#^(7)100#100
  5880.  
  5881.  
  5882.  
  5883.  
  5884. ...
  5885.  
  5886.  
  5887.  
  5888.  
  5889. tethrahexonicor-doplus = E100#^^#^(7)100#^^#^(7)100
  5890.  
  5891.  
  5892.  
  5893.  
  5894. ...
  5895.  
  5896.  
  5897.  
  5898.  
  5899. deutero-tethrahexonicor = E100#^^#^(7)*#^^#^(7)100
  5900.  
  5901.  
  5902.  
  5903.  
  5904. ...
  5905.  
  5906.  
  5907.  
  5908.  
  5909. tethrahexonifact = E100(#^^#^(7))^#100
  5910.  
  5911.  
  5912.  
  5913.  
  5914. ...
  5915.  
  5916.  
  5917.  
  5918.  
  5919. deutetrated-tethrahexonicor = E100(#^^#^(7))^(#^^#^(7))100
  5920.  
  5921.  
  5922.  
  5923.  
  5924. ...
  5925.  
  5926.  
  5927.  
  5928.  
  5929. terrible tethrahexonicor = E100(#^^#^(7))^^#100
  5930.  
  5931.  
  5932.  
  5933.  
  5934. ...
  5935.  
  5936.  
  5937.  
  5938.  
  5939. territerated tethrahexonicor = E100(#^^#^(7))^^#>#100
  5940.  
  5941.  
  5942.  
  5943.  
  5944. ...
  5945.  
  5946.  
  5947.  
  5948.  
  5949. duturreted-territethrahexonicor = E100(#^^#^(7))^^#>(#^^#^(7))^^#100
  5950.  
  5951.  
  5952.  
  5953.  
  5954. ...
  5955.  
  5956.  
  5957.  
  5958.  
  5959. terrisquared-tethrahexonicor = E100(#^^#^(7))^^##100
  5960.  
  5961.  
  5962.  
  5963.  
  5964. terricubed-tethrahexonicor = E100(#^^#^(7))^^###100
  5965.  
  5966.  
  5967.  
  5968.  
  5969. territesserated-tethrahexonicor = E100(#^^#^(7))^^####100
  5970.  
  5971.  
  5972.  
  5973.  
  5974. terripenterated-tethrahexonicor = E100(#^^#^(7))^^#^(5)100
  5975.  
  5976.  
  5977.  
  5978.  
  5979. terrihexerated-tethrahexonicor = E100(#^^#^(7))^^#^(6)100
  5980.  
  5981.  
  5982.  
  5983.  
  5984. tethra-deuterhexonicor = E100(#^^#^(7))^^#^(7)100
  5985.  
  5986.  
  5987.  
  5988.  
  5989. ...
  5990.  
  5991.  
  5992.  
  5993.  
  5994. tethra-iterhexonicor = E100#^^#^(7)>#100
  5995.  
  5996.  
  5997.  
  5998.  
  5999. ...
  6000.  
  6001.  
  6002.  
  6003.  
  6004. duturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)100
  6005.  
  6006.  
  6007.  
  6008.  
  6009. triturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)100
  6010.  
  6011.  
  6012.  
  6013.  
  6014. tetraturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)>#^^#^(7)100
  6015.  
  6016.  
  6017.  
  6018.  
  6019. ...
  6020.  
  6021.  
  6022.  
  6023.  
  6024.  
  6025.  
  6026.  
  6027.  
  6028.  
  6029. tethra-dekonicor = E100#^^#^#11
  6030.  
  6031.  
  6032.  
  6033.  
  6034.  
  6035. tethrahexonicor = E100#^^#^#7
  6036.  
  6037.  
  6038.  
  6039.  
  6040. (from tetration + polyecton )
  6041.  
  6042.  
  6043.  
  6044.  
  6045.  
  6046. grand tethrahexonicor = E100#^^#^(7)100#2
  6047.  
  6048.  
  6049.  
  6050.  
  6051. ...
  6052.  
  6053.  
  6054.  
  6055.  
  6056. grangol-carta-tethrahexonicor = E100#^^#^(7)100#100
  6057.  
  6058.  
  6059.  
  6060.  
  6061. ...
  6062.  
  6063.  
  6064.  
  6065.  
  6066. tethrahexonicor-doplus = E100#^^#^(7)100#^^#^(7)100
  6067.  
  6068.  
  6069.  
  6070.  
  6071. ...
  6072.  
  6073.  
  6074.  
  6075.  
  6076. deutero-tethrahexonicor = E100#^^#^(7)*#^^#^(7)100
  6077.  
  6078.  
  6079.  
  6080.  
  6081. ...
  6082.  
  6083.  
  6084.  
  6085.  
  6086. tethrahexonifact = E100(#^^#^(7))^#100
  6087.  
  6088.  
  6089.  
  6090.  
  6091. ...
  6092.  
  6093.  
  6094.  
  6095.  
  6096. deutetrated-tethrahexonicor = E100(#^^#^(7))^(#^^#^(7))100
  6097.  
  6098.  
  6099.  
  6100.  
  6101. ...
  6102.  
  6103.  
  6104.  
  6105.  
  6106. terrible tethrahexonicor = E100(#^^#^(7))^^#100
  6107.  
  6108.  
  6109.  
  6110.  
  6111. ...
  6112.  
  6113.  
  6114.  
  6115.  
  6116. territerated tethrahexonicor = E100(#^^#^(7))^^#>#100
  6117.  
  6118.  
  6119.  
  6120.  
  6121. ...
  6122.  
  6123.  
  6124.  
  6125.  
  6126. duturreted-territethrahexonicor = E100(#^^#^(7))^^#>(#^^#^(7))^^#100
  6127.  
  6128.  
  6129.  
  6130.  
  6131. ...
  6132.  
  6133.  
  6134.  
  6135.  
  6136. terrisquared-tethrahexonicor = E100(#^^#^(7))^^##100
  6137.  
  6138.  
  6139.  
  6140.  
  6141. terricubed-tethrahexonicor = E100(#^^#^(7))^^###100
  6142.  
  6143.  
  6144.  
  6145.  
  6146. territesserated-tethrahexonicor = E100(#^^#^(7))^^####100
  6147.  
  6148.  
  6149.  
  6150.  
  6151. terripenterated-tethrahexonicor = E100(#^^#^(7))^^#^(5)100
  6152.  
  6153.  
  6154.  
  6155.  
  6156. terrihexerated-tethrahexonicor = E100(#^^#^(7))^^#^(6)100
  6157.  
  6158.  
  6159.  
  6160.  
  6161. tethra-deuterhexonicor = E100(#^^#^(7))^^#^(7)100
  6162.  
  6163.  
  6164.  
  6165.  
  6166. ...
  6167.  
  6168.  
  6169.  
  6170.  
  6171. tethra-iterhexonicor = E100#^^#^(7)>#100
  6172.  
  6173.  
  6174.  
  6175.  
  6176. ...
  6177.  
  6178.  
  6179.  
  6180.  
  6181. duturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)100
  6182.  
  6183.  
  6184.  
  6185.  
  6186. triturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)100
  6187.  
  6188.  
  6189.  
  6190.  
  6191. tetraturreted-tethrahexonicor = E100#^^#^(7)>#^^#^(7)>#^^#^(7)>#^^#^(7)100
  6192.  
  6193.  
  6194.  
  6195.  
  6196. ...
  6197.  
  6198.  
  6199.  
  6200.  
  6201.  
  6202. tethraspace group
  6203.  
  6204.  
  6205.  
  6206.  
  6207.  
  6208. tethrahectonicor = E100#^^#^#101
  6209.  
  6210.  
  6211.  
  6212.  
  6213. tethrachilonicor = E100#^^#^#1001
  6214.  
  6215.  
  6216.  
  6217.  
  6218. tethramyrionicor = E100#^^#^#10,001
  6219.  
  6220.  
  6221.  
  6222.  
  6223. numbers in need of names
  6224.  
  6225.  
  6226.  
  6227.  
  6228. E100(#^^#^#)^^#^#100
  6229.  
  6230.  
  6231.  
  6232.  
  6233. E100((#^^#^#)^^#^#)^^#^#100
  6234.  
  6235.  
  6236.  
  6237.  
  6238. E100#^^(#^#)>#100
  6239.  
  6240.  
  6241.  
  6242.  
  6243. E100#^^(#^#)>#^^#^#100
  6244.  
  6245.  
  6246.  
  6247.  
  6248. E100#^^(#^#*#)100
  6249.  
  6250.  
  6251.  
  6252.  
  6253. E100#^^(#^#*##)100
  6254.  
  6255.  
  6256.  
  6257.  
  6258. E100#^^(#^#*#^#)100
  6259.  
  6260.  
  6261.  
  6262.  
  6263. E100#^^#^##100
  6264.  
  6265.  
  6266.  
  6267.  
  6268. E100#^^#^###100
  6269.  
  6270.  
  6271.  
  6272.  
  6273. E100#^^#^#^#100
  6274.  
  6275.  
  6276.  
  6277.  
  6278. E100#^^#^#^#^#100
  6279.  
  6280.  
  6281.  
  6282.  
  6283.  
  6284. tethrarxitri = E100#^^#^^#100 (also tethrarxitri from “arx” latin for tower)
  6285.  
  6286. tethrarxiquad = E100#^^#^^#^^#100
  6287.  
  6288. tethrarxiquid = E100#^^^#5
  6289.  
  6290. tethrarxissid = E100#^^^#6
  6291.  
  6292. tethrarxissip= E100#^^^#7
  6293.  
  6294. tethrarxi-ogd = E100#^^^#8
  6295.  
  6296. tethrarxideck = E100#^^^#10
  6297.  
  6298. pentacularex = E100#^^^#100 (also tethraxihecate)
  6299.  
  6300. pentacthulum = E100#^^^#100
  6301.  
  6302. pentacthulusquare = E100#^^^##100
  6303.  
  6304. pentacthulucubor = E100#^^^###100
  6305.  
  6306. pentacthulutesseractus = E100#^^^####100
  6307.  
  6308. pentacthulupenteractus = E100#^^^#^#5
  6309.  
  6310. pentacthuluhexeractus = E100#^^^#^#6
  6311.  
  6312. ...
  6313.  
  6314. pentarxitri = E100#^^^#^^^#100
  6315.  
  6316. hexhaxulum = E100#^^^^#100
  6317.  
  6318. hexhaxulusquare = E100#^^^^##100
  6319.  
  6320. hexhaxulucubor = E100#^^^^###100
  6321.  
  6322. hexarxitri = E100#^^^^#^^^^#100
  6323.  
  6324. ...
  6325.  
  6326. tethrarxichill = E100#^^^#1000
  6327.  
  6328. tethrarximyr = E100#^^^#10,000
  6329.  
  6330. tethrarxi-octad = E100#^^^#100,000,000
  6331.  
  6332. tethrarxi-sedeniad = E100#^^^#10,000,000,000,000,000
  6333.  
  6334. grand pentacularex = E100#^^^#100#2 = E100#^^^#pentacularex
  6335.  
  6336. double grand pentacularex = E100#^^^#100#3
  6337.  
  6338. triple grand pentacularex = E100#^^^#100#4
  6339.  
  6340. pentacula-expoundum = E100#^^^#^#100
  6341.  
  6342. pentacula-hyperia-expoundum = E100#^^^#^#^#100
  6343.  
  6344. pentacula-duhyperia-expoundum = E100#^^^#^#^#^#100
  6345.  
  6346. pentacula-tethrulex = E100#^^^#^^#100
  6347.  
  6348. grand pentacula-tethrulex = E100#^^^#^^#pentacula-tethrulex
  6349.  
  6350. joe pellinger = E100#^^^#^^#^#199,999,999
  6351.  
  6352. pentaxitri = E100#^^^#^^^#100
  6353.  
  6354. pentaxiquad = E100#^^^#^^^#^^^#100
  6355.  
  6356. pentaxiquid = E100#^^^^#5
  6357.  
  6358. pentaxissid= E100#^^^^#6
  6359.  
  6360. pentaxissip = E100#^^^^#7
  6361.  
  6362. pentaxi-ogd = E100#^^^^#8
  6363.  
  6364. hexhaxularex = E100#^^^^#100
  6365.  
  6366. heptacularex = E100#^^^^^#100
  6367.  
  6368. octacularex = E100#^^^^^^#100
  6369.  
  6370. goliath = E100#{#}#10 = E100#^^^^^^^^^^#100
  6371.  
  6372. godsgodgulus = E100#{#}#100 = E100#^^^…^^^#100 w/100 ^s
  6373.  
  6374. colossus = E100#{#}#50,000,000,000,000,000
  6375.  
  6376. grand godsgodgulus = E100#{#}#100#2 = E100#{#}#godsgodgulus
  6377.  
  6378. blasphemorgulog = E100{#,#,1,2}100
  6379.  
  6380. grand blasphemorgulog = E100{#,#,1,2}100#2
  6381.  
  6382. sprach Zarathustra = E100{#,#(1)2}50,000,000,000,000,000
  6383.  
  6384. Thus sprach Zarathustra = E100{#,#(1)2}50,000,000,000,000,000#2
  6385.  
  6386. Zarathustra-Grid = E100{#,#(2)2}50,000,000,000,000,000
  6387.  
  6388. Zarathustra-Cube = E100{#,#(3)2}50,000,000,000,000,000
  6389.  
  6390. Zarathustra-Tess = E100{#,#(4)2}50,000,000,000,000,000
  6391.  
  6392.  
  6393.  
  6394.  
  6395.  
  6396.  
  6397.  
  6398.  
  6399.  
  6400.  
  6401.  
  6402.  
  6403.  
  6404. ########################################################
  6405.  
  6406. ########################################################
  6407.  
  6408. ########################################################
  6409.  
  6410. ########################################################
  6411.  
  6412. tethriter-tetraplux = E100#^^#>#^^#100 (also tethri-staculardeus)
  6413.  
  6414. tethri-staculartruce = E100#^^#>#^^#>#^^#100
  6415.  
  6416. tethri-stacularquad = E100#^^#>#^^#>#^^#>#^^#100
  6417.  
  6418. tethri-stacularquid = E100#^^##5
  6419.  
  6420. tethricross = E100#^^##100
  6421.  
  6422. grangol-carta-tethricross = E100#^^##100#100
  6423.  
  6424. godgahlah-carta-tethricross = E100#^^##100#^#100
  6425.  
  6426. tethrathothi-carta-tethricross = E100#^^##100#^^#100
  6427.  
  6428. tethriterator-carta-tethricross = E100#^^##100#^^#>#100
  6429.  
  6430. tristo-tethricross = E100#^^##100#^^##100
  6431.  
  6432. deutero-tethricross = E100#^^##*#^^##100
  6433.  
  6434. trito-tethricross = E100#^^##*#^^##*#^^##100
  6435.  
  6436. terri-tethricross = E100(#^^##)^^#100
  6437.  
  6438. territer-tethricross = E100(#^^##)^^#>#100
  6439.  
  6440. terriditer-tethricross = E100(#^^##)^^#>(#+#)100
  6441.  
  6442. tethricube = E100#^^###100 (also tethrurricybus from “turri cybus” latin for “tower cube”)
  6443.  
  6444. tethritess = E100#^^####100
  6445.  
  6446. tethripent = E100#^^#^#5
  6447.  
  6448. tethrihex = E100#^^#^#6
  6449.  
  6450. tethrihept = E100#^^#^#7
  6451.  
  6452. tethri-ocht = E100#^^#^#8
  6453.  
  6454. tethrihecate = E100#^^#^#100
  6455.  
  6456. tethrichill = E100#^^#^#1000
  6457.  
  6458. tethrimyr = E100#^^#^#10,000
  6459.  
  6460. tethri-octad = E100#^^#^#100,000,000
  6461.  
  6462. tethri-sedeniad = E100#^^#^#10,000,000,000,000,000
  6463.  
  6464. tethrarxitri = E100#^^#^^#100 (also tethrarxitri from “arx” latin for tower)
  6465.  
  6466. tethrarxiquad = E100#^^#^^#^^#100
  6467.  
  6468. tethrarxiquid = E100#^^^#5
  6469.  
  6470. tethrarxissid = E100#^^^#6
  6471.  
  6472. tethrarxissip= E100#^^^#7
  6473.  
  6474. tethrarxi-ogd = E100#^^^#8
  6475.  
  6476. tethrarxideck = E100#^^^#10
  6477.  
  6478. pentacularex = E100#^^^#100 (also tethraxihecate)
  6479.  
  6480. pentacthulum = E100#^^^#100
  6481.  
  6482. pentacthulusquare = E100#^^^##100
  6483.  
  6484. pentacthulucubor = E100#^^^###100
  6485.  
  6486. pentacthulutesseractus = E100#^^^####100
  6487.  
  6488. pentacthulupenteractus = E100#^^^#^#5
  6489.  
  6490. pentacthuluhexeractus = E100#^^^#^#6
  6491.  
  6492. ...
  6493.  
  6494. pentarxitri = E100#^^^#^^^#100
  6495.  
  6496. hexhaxulum = E100#^^^^#100
  6497.  
  6498. hexhaxulusquare = E100#^^^^##100
  6499.  
  6500. hexhaxulucubor = E100#^^^^###100
  6501.  
  6502. hexarxitri = E100#^^^^#^^^^#100
  6503.  
  6504. ...
  6505.  
  6506. tethrarxichill = E100#^^^#1000
  6507.  
  6508. tethrarximyr = E100#^^^#10,000
  6509.  
  6510. tethrarxi-octad = E100#^^^#100,000,000
  6511.  
  6512. tethrarxi-sedeniad = E100#^^^#10,000,000,000,000,000
  6513.  
  6514. grand pentacularex = E100#^^^#100#2 = E100#^^^#pentacularex
  6515.  
  6516. double grand pentacularex = E100#^^^#100#3
  6517.  
  6518. triple grand pentacularex = E100#^^^#100#4
  6519.  
  6520. pentacula-expoundum = E100#^^^#^#100
  6521.  
  6522. pentacula-hyperia-expoundum = E100#^^^#^#^#100
  6523.  
  6524. pentacula-duhyperia-expoundum = E100#^^^#^#^#^#100
  6525.  
  6526. pentacula-tethrulex = E100#^^^#^^#100
  6527.  
  6528. grand pentacula-tethrulex = E100#^^^#^^#pentacula-tethrulex
  6529.  
  6530. joe pellinger = E100#^^^#^^#^#199,999,999
  6531.  
  6532. pentaxitri = E100#^^^#^^^#100
  6533.  
  6534. pentaxiquad = E100#^^^#^^^#^^^#100
  6535.  
  6536. pentaxiquid = E100#^^^^#5
  6537.  
  6538. pentaxissid= E100#^^^^#6
  6539.  
  6540. pentaxissip = E100#^^^^#7
  6541.  
  6542. pentaxi-ogd = E100#^^^^#8
  6543.  
  6544. hexhaxularex = E100#^^^^#100
  6545.  
  6546. heptacularex = E100#^^^^^#100
  6547.  
  6548. octacularex = E100#^^^^^^#100
  6549.  
  6550. goliath = E100#{#}#10 = E100#^^^^^^^^^^#100
  6551.  
  6552. godsgodgulus = E100#{#}#100 = E100#^^^…^^^#100 w/100 ^s
  6553.  
  6554. colossus = E100#{#}#50,000,000,000,000,000
  6555.  
  6556. grand godsgodgulus = E100#{#}#100#2 = E100#{#}#godsgodgulus
  6557.  
  6558. blasphemorgulog = E100{#,#,1,2}100
  6559.  
  6560. grand blasphemorgulog = E100{#,#,1,2}100#2
  6561.  
  6562. sprach Zarathustra = E100{#,#(1)2}50,000,000,000,000,000
  6563.  
  6564. Thus sprach Zarathustra = E100{#,#(1)2}50,000,000,000,000,000#2
  6565.  
  6566. Zarathustra-Grid = E100{#,#(2)2}50,000,000,000,000,000
  6567.  
  6568. Zarathustra-Cube = E100{#,#(3)2}50,000,000,000,000,000
  6569.  
  6570. Zarathustra-Tess = E100{#,#(4)2}50,000,000,000,000,000
  6571.  
  6572. ips – greek for “heighten”
  6573.  
  6574. arx – latin for “castle”
  6575.  
  6576. turri – latin for “tower”
  6577.  
  6578. laniatus – latin for “excellent”
  6579.  
  6580. excellens – excellence (latin)
  6581. eximus – extraordinary (latin)
  6582.  
  6583.  
  6584.  
  6585.  
  6586.  
  6587.  
  6588.  
  6589.  
  6590.  
  6591.  
  6592.  
  6593.  
  6594.  
  6595. pentacular = E100#^^^#100
  6596.  
  6597.  
  6598.  
  6599. hexhaxular = E100#^^^^#100
  6600.  
  6601.  
  6602.  
  6603. heptacular = E100#^^^^^#100
  6604.  
  6605.  
  6606.  
  6607. octacular = E100#^^^^^^#100
  6608.  
  6609.  
  6610.  
  6611. godsgodgulus = E100#^^^^^^^^^^......^^^^^^^^^^#100 w/100 ^s
  6612.  
  6613.  
  6614.  
  6615. E100#{#}#100 = E100#{100}#100
  6616.  
  6617.  
  6618.  
  6619. (#{#}#)^^#
  6620.  
  6621.  
  6622.  
  6623. (#{#}#)^^^#
  6624.  
  6625.  
  6626.  
  6627. (#{#}#){#}#
  6628.  
  6629.  
  6630.  
  6631. #{#}#>#
  6632.  
  6633.  
  6634.  
  6635. #{#}##
  6636.  
  6637.  
  6638.  
  6639. #{#}###
  6640.  
  6641.  
  6642.  
  6643. #{#}#^#
  6644.  
  6645.  
  6646.  
  6647. #{#}#{#}#{#}#{#}#
  6648.  
  6649.  
  6650.  
  6651. #{#}^#
  6652.  
  6653.  
  6654.  
  6655. #{#}^^#
  6656.  
  6657.  
  6658.  
  6659. #{#}^^^#
  6660.  
  6661.  
  6662.  
  6663. #{#}^^^^#
  6664.  
  6665.  
  6666. #{#+#}#
  6667.  
  6668.  
  6669.  
  6670. #{#+#+#}#
  6671.  
  6672.  
  6673.  
  6674. #{##}#
  6675.  
  6676.  
  6677.  
  6678. #{###}#
  6679.  
  6680.  
  6681.  
  6682. #{#^#}#
  6683.  
  6684.  
  6685.  
  6686. #{#^^#}#
  6687.  
  6688.  
  6689.  
  6690. #{#^^^#}#
  6691.  
  6692.  
  6693.  
  6694. #{#{#}#}#
  6695.  
  6696.  
  6697.  
  6698. ...
  6699.  
  6700.  
  6701.  
  6702. blasphemorgulog = E100{#,#,1,2}100
  6703.  
  6704.  
  6705.  
  6706. grand blasphemorgulog = E100{#,#,1,2}100#2
  6707.  
  6708.  
  6709.  
  6710.  
  6711.  
  6712.  
  6713.  
  6714.  
  6715.  
  6716.  
  6717.  
  6718.  
  6719.  
  6720.  
  6721.  
  6722.  
  6723.  
  6724.  
  6725.  
  6726.  
  6727.  
  6728.  
  6729.  
  6730.  
  6731.  
  6732.  
  6733.  
  6734.  
  6735.  
  6736.  
  6737.  
  6738.  
  6739.  
  6740.  
  6741.  
  6742.  
  6743.  
  6744.  
  6745.  
  6746.  
  6747.  
  6748.  
  6749.  
  6750.  
  6751.  
  6752.  
  6753.  
  6754.  
  6755.  
  6756.  
  6757.  
  6758. αβγδεζηθικλμνξοπρςστυφχψω
  6759.  
  6760. αβγδεζηθικλμνξοπρςστυφχψω
  6761.  
  6762. gulog (a logarithm deals with orders of magnitude a gulogarithm deals with a number of googological magnitude!)
  6763.  
  6764.  
  6765.  
  6766.  
  6767. godsgodgulog
  6768.  
  6769. blasphemorgulog
  6770.  
  6771.  
  6772.  
  6773.  
  6774. gulus - for numbers of the googol family of size greater than or equal to order type w^w^w
  6775.  
  6776.  
  6777.  
  6778.  
  6779. joe pellinger
  6780.  
  6781.  
  6782.  
  6783.  
  6784. Centurion / Grand Centurion / Super Centurion
  6785.  
  6786.  
  6787.  
  6788.  
  6789. Colossus
  6790.  
  6791.  
  6792.  
  6793.  
  6794. Colossulus
  6795.  
  6796.  
  6797.  
  6798.  
  6799. Goliath
  6800.  
  6801.  
  6802.  
  6803.  
  6804. Og (A name of a giant)
  6805.  
  6806.  
  6807.  
  6808.  
  6809. Nephilim
  6810.  
  6811.  
  6812.  
  6813.  
  6814. Nephilus-Megalosus
  6815.  
  6816.  
  6817.  
  6818.  
  6819. Brobdingnagulus
  6820.  
  6821.  
  6822.  
  6823.  
  6824. Gargantua
  6825.  
  6826.  
  6827.  
  6828.  
  6829. Pantagruel
  6830.  
  6831.  
  6832.  
  6833.  
  6834. Tremendagulus
  6835.  
  6836.  
  6837.  
  6838.  
  6839. Godsgodgulus
  6840.  
  6841.  
  6842.  
  6843.  
  6844. blasmephorgulus
  6845.  
  6846.  
  6847.  
  6848.  
  6849. gralgathor
  6850.  
  6851.  
  6852.  
  6853.  
  6854. tethrathor
  6855.  
  6856.  
  6857.  
  6858.  
  6859. tetritathor
  6860.  
  6861.  
  6862.  
  6863.  
  6864. teritathor
  6865.  
  6866.  
  6867.  
  6868.  
  6869. iteratathor
  6870.  
  6871.  
  6872.  
  6873.  
  6874. tetration + iterator -->
  6875.  
  6876.  
  6877.  
  6878.  
  6879. tethriterator = E100#^^#>#100 (alternative name for tethrathoth ba'al)
  6880.  
  6881.  
  6882.  
  6883.  
  6884. grand tethriterator = E100#^^#>#100#2 (alt. of Great and Terrible tethrathoth)
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