There are three states of existence: **Void**, **Something**, and **Infinity**.

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Everything that can be measured or counted can be described as a state between **Void** and **Infinity**.

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**Void** can be represented with the character **0**, or with the words **zero**, **nil**, **null**, or **void**. This is the absence of value.

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**Something** can be represented with the character **1**, or with the words **one**, **thing**, or **something**. This is the state that exists between Void and Infinity.

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**Infinity** can be represented with the character **∞**, or the words **infinity**, **infinite**, or **everything**. This has immeasurable value.

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Numbers represent a sum, grouping, or combination of **Void**, **Something**, and **Infinity**.

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When measuring things that exist, we can use **numbers**. Numbers are composed of description of a state and a **direction**.

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A positive value moves the amount we are describing further from **Void** toward **Infinity**.

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A negative value moves a value the amount we are describing further from **Inftinity** toward **Void**.

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**Void** and **Void** grouped together will have no value and are the same as **Void** alone.

(0 0) = 0
(~~0~~ 0) = 0
(0) = 0

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**Void** and **Something** grouped together will have the same value as **Something** alone.

(0 1) = 1
(~~0~~ 1) = 1
(1) = 1

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**Void** and **Infinity** grouped together will have the same value as **Infinity** alone.

(0 ∞) = ∞
(~~0~~ ∞) = ∞
(∞) = ∞

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Something and Something grouped together are the integers. We use characters like 2 to represent Something and Something, or 3 to represent Something and Something and Something.

(1 1) = 2

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Something and Infinity grouped together will have the same value as Infinity alone.

(1 ∞) = ∞
(~~1~~ ∞) = ∞
(∞) = ∞

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Infinity and Infinity grouped together will have the same value as Infinity alone.

(∞ ∞) = ∞
(~~∞~~ ∞) = ∞

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Even though we can't measure or count Infinity, we can still reason with it to uncover truths and relationships that are true whenever or wherever tested.

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Because any value we can describe has the same amount as that same value combined with Void, Void is ever-present and just as incalculable as Infinity.

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Addition is the grouping of representations of states together and moving the number you are describing from void toward infinity by that amount.

2 + 2 = ((1 1) (1 1))
2 + 2 = (1 1 1 1)

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Subtraction is the grouping of representations of states together and moving the number you are describing from infinity toward void by that amount.

4 - 2 = ((1 1 1 1) -1 -1)
4 - 2 = ((1 1) ~~(1 1)~~ ~~(-1 -1)~~)
4 - 2 = (1 1)

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Multiplication is a shorthand for addition. Multiplication by a fraction is a shorthand for division.

2 * 2 = (2 2)
2 * 2 = ((1 1) (1 1))
2 * 2 = (1 1 1 1)

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Division is multiplication by a fraction.

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Fractions are the states between Void and Something.

0 <--- 1 : (1 1) ---> 1 : ∞

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Decimals are numbers that represent a grouping of integers and fractions.

(1 5/10) = 1.5
(1 1/2) = 1.5

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The Number Line is a linear representation of possible states between negative infinity, negative something, void, something, and infinity.

```
-∞ <------- -1 --------- 0 --------- 1 -------> ∞

   integers    fractions   fractions   integers
```