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Chapter 11.6 - Counting Theory (very rough draft)

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  1. ~-_-*&~(AL) - s'TC - Truth and vision by OnlyNess; {xXMooNCryXxX) - CT's - (LA)~-_-*&~  \
  2.  
  3. Subject : Counting Theory, Mathemathics.  
  4. What we'll go over and learn in this text: how to count numbers, (duh!)
  5.  
  6. Suppose a teacher has 5 books, but she only wants to place 3 of them out for display. How many arragements of 3 books is possible?
  7. first of all I presume you are aware of the fallowing mathemathical concepts.
  8.  
  9. the fundamental theorom of counting : I will keep this definition strict, rigorous and straight from the text, never EVER bounce around or rejoice with your functions/formulas/concrete knowledge you must have comulatative discipline to do these calculations off hand, if you need a calculator to do it, then I beg you, just stop doing mathemathics all together.
  10.  
  11. In the roads example in my listed methods, he uses 3 roads from chicago to chicago (streets within chicago, confusing I know) Don't just make visual connections, make audio and visual connections, syntatic connections, memory connections, learn to manipulate your own knowledge and weild it like a sword. get INTELLIGENCE. YES IT IS AQUIRED AND I STAND BY THAT BELIEF WITH ALL CONFIDENCE.
  12.  
  13. example: if there are 3 roads \emph from irving park to belmont (that's a damned lie and I know it! just play along anyways); and there are also 2 roads belmont to sheffield, how many ways can one travel from irving park to belmont to sheffeild by way of belmont \emph(chosen street is intermediate between the two others if you must know).
  14.  
  15. Here, each choice of road is an
  16.  
  17. Here each
  18.  
  19. Supposition, consideration : Have character and go at it.
  20.  
  21. example: if there are 3 roads \emph from irving park to belmont (that's a damned lie and I know it! just play along anyways); and there are also 2 roads belmont to sheffield, how many ways can one travel from irving park to belmont to sheffeild by way of belmont \emph(chosen street is intermediate between the two others if you must know).
  22.  
  23. You must physically with hand write these things out, get it OUT there, so you can view it, it becomes so much EASIER, I suggest using graphs and visuals to describe a lot of these events, I also assume you know definition of permutation, event, independent event condition and a myrad of other matryotic matryoshkish hibbur-wee-j00. etc words, I will provide those within this prevailing text as well.
  24.  
  25. definition of event: an even is independent if it isn't influenced by other events, now the /emph here is the initial value problem, we are confronted with a question, just exactly how do we start? well, ask yourself this, what is the event about? what is it's "aboutness"??? i'll tell ya what it is, it's usually the items they have on sale man. if you have 5 dollars and want to buy some fucking dorritos for a dollar each (discluding tax garnishes) considering you aren't a complete jackass who buys it all at once and burdens his fellow neighbor I would assume you'd do it in ORDER, you have (5)dollars "r" and want (???) number of bags of dorritos "n", you must solve for the number of n desired or wanted or w/e. I want 5 bags of dorritos buying them one bag at a time, 5 transactions occur, therefor there are 5 events, you can derive conclusions on this simple method all fucking day if you want, the point is you must solve for the number of n.
  26.  
  27. you do this simply by considering the value of r, which is 5, and using that as an abstract tree tree diagram. placeholders
  28.  
  29. method 1:
  30.  
  31. 1.) count the number of events.
  32.  
  33. how many times will an action occur? think about it. she places the initial book, thats 1. She places another, that's 2. we have 2 books now we place the last we have a total of 3 books and 3 events.
  34.  
  35. 2.) Ask yourself, "what is the total amount of books (r) versus the amount of n (the total amount "(displayed)"<condition of r.)".
  36.  
  37. 3.) we now know that 5 and 3 are important numbers r and n respectively, with r > being greater than or equal to n.  but also keep in mind, this inequality can vary, it's not fixed, r can be less, greater, it can be anything, it varies from case to case. so you should consider this in such a way you would consider the methodology of finding roots, tedius, long,drawn out and over bearing but it pays off because the practice makes you quick witted as fuck.
  38.  
  39. the answer becomes clear, 3 events = 3 placement values, we start from the top and go down a corresponding event until we have what is now presented,
  40.  
  41. 5 x 4 (20) x 3(???) = 60, (profit!) total amount of possible arrangements.
  42.  
  43. \big\bold{mathrm}method 2: drawing.
  44.  
  45. example: if there are 3 roads \emph from irving park to belmont (that's a damned lie and I know it! just play along anyways); and there are also 2 roads belmont to sheffield, how many ways can one travel from irving park to belmont to sheffeild by way of belmont \emph(chosen street is intermediate between the two others if you must know).
  46.  
  47. you would draw a tree diagram, and pick a starting point, then next to it, draw 3 dots which represent the amount of possible ways to get from point a to point b, in this case it is GIVEN to us so methodology for finding that won't be covered, (distance formula dumbass)
  48.  
  49. you would then draw out 2 sub-branches from the 3 belmonts which are the sheffields, it's much easier to comprehend this if you just look at it from a photographic point of view,
  50.  
  51. irving park is a street name, we assume based on no evidence that there exists 3 and only 3 ways to get to belmont \emph from irving park, I place an emphasis on from because time tense words can really give you big time discalcula.
  52.  
  53.  
  54.  
  55. (3 ways to belmont from irving park)
  56.  
  57.  
  58.  
  59.  
  60.  
  61.  
  62.  
  63.                                                                                   |           Sheffeild            
  64.                                                    |       Belmont              
  65.  
  66.                                                                                   |          Sheffeild
  67.  
  68.  
  69.  
  70.                                                                                   |           Sheffeild    
  71. Irving Park(starting point)        |      Belmont          
  72.                                                          
  73.                                                                                   |           Sheffeild                          
  74.  
  75.  
  76.  
  77.                                                                                  |           Sheffeild    
  78.                                                  |      Belmont          
  79.                                                          
  80.  
  81.                                                                                 |            Sheffeild                          
  82.  
  83.  
  84. 1 x 3 = 8.
  85.  
  86.  
  87. ;apply \bold method 3. It is wise to choose the intermediary for common senses reasoning however for this one I will show various ways of approaching it, including "the other way round'"
  88.  
  89. Wish this text pad had a function which withdrew value of place holders so I could just fill in the balnks with that ctrl + v status. great idea I think, anyWHO....]
  90.  
  91. Sheffeild(8) Irving park (1) Belmont (6)
  92.  
  93. Method 3: solving by algebraic intuition.
  94.  
  95. disclude the destination point, and place it's value on the equals sign, if i had to use my \emph better judgement I'd say this order Irving -> belmont -> sheffeild where belmont is intermidiary, irving is starting point and sheffeild is destination point. destination = ON THE OTHER SIDE OF =. REMEMBER IT.
  96.  
  97. 1 x 6 = 8
  98.  
  99.  
  100.  
  101.                                               |      Belmont    
  102.  
  103.  
  104. becomes,... =
  105.  
  106.  
  107.  
  108.  
  109.  
  110. !!!!!!!!!!!!!!!!~-_-*&~/////////////////////end***~*~*~*~*~*~}~*|~*~~|*~*|*~*!!!!!!!!!!!!!!!!
  111.  
  112.                            ..  .   .  . it   comes  from  where it ends ..  .   .  .
  113.        .. . and that is god's honest reaction to answer which predates it's questioning. . ..
  114.  
  115.                     "The Love of survival is the only way to ensure the survival of love"
  116.             "Creativity, ingenous, intuition; and the ability shape it with mathemathics, skill, and raw talent."
  117.  
  118.  
  119.             ~!AliasNation,TheIndegenous,xat.com/flirt,xat.com/lobby,theelite.net,thecorrupt,teampoison,
  120. thesinned, all my enemies, friends, lovers, foes you know who you are, I mean you no harm and infact I wish
  121. to try to make the means again, and I' m sorry for my black hatted usage of computer equipment over the years. ... "
  122.  
  123.  
  124. \documentclass{article}
  125. \usepackage{amsmath}
  126. \begin{document}
  127.  
  128. \begin{displaymath}
  129. {F}(x,y)=0\quad\mathrm(and)\quad
  130. \left | \begin{array}{ccc}
  131. F_{xx}' ' & F_{xy}' ' & F_{x}' \\
  132. F_{yx}' '  & F_{yy}' ' & F_{y}' \\
  133. F_{x}'      & F_{y}' & 0
  134.        \end{array} \right| 0
  135. \end{displaymath}
  136.  
  137.  
  138. \begin{displaymath} \mathrm(it may be a good idea to study each symbol or type of operation individually and commutatively in order to get a better understanding of it. fallow me at MoonCyde@youtube.com)
  140. \left 1 \pm\,+\dfrac {1}{2}\mathrm(intersection is cap)\cap \quad\mathrm(unison is cup\, \cup \end{displaymath}
  141.  
  142. \end{displaymath}
  143.  
  144. \end{document}
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