# NUMBERS_15_NOVEMBER_2022_COPY

NUMBERS_15_NOVEMBER_2022_COPY

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NUMBERS

“Nature is identical to infinity.” – karbytes

“Nature is not identical to infinity. Infinity is a concept which occurs inside of nature.” – karbytes

The following terms and their respective definitions (and elaborating paragraphs) attempt to enumerate all possible quantities (i.e. numbers). A number is a precisely communicable piece of information which represents exactly one discrete quantity.

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ONE: (represented by the character 1) the smallest natural number; the length of the line segment whose endpoints are adjacent integers within a Cartesian grid.

ZERO: (represented by the character 0) the absence of quantitative measurement; the integer which represents the halfway point between negative one (-1) and one (1); the point which is the same distance apart from the point labeled -1 as it is apart from the point labeled 1 on the same Cartesian grid axis.

NUMBER: a piece of information which represents a finite quantity; a piece of information which can be encoded as a finite sequence of binary digits (i.e. 0 and 1).

INFINITY: a direction of perpetual increase; the instantiation of limitlessly many copies of exactly one pattern; the instantiation of limitlessly many objects such that each one of those objects is phenomenally distinct from every other one of those objects; a “quantity” which is larger than or equal to the sum of all positive numbers (and that “quantity” is not technically a number and there are limitelessly many numbers which would comprise that hypothetical sum (which means that the sum is also technically not a number because that sum cannot be computed by an information processing agent within a finite interval of time if the process of adding each positive number to a running total takes a finite and nonzero amount of time and a finite and nonzero amount of energy to complete)).

NATURAL_NUMBER: an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of every unique sum of one or multiple instances of one.

```length("") = 0. // zero (i.e. the quantity which symbolically represents the detection of some noumenon)
length("X") = 1. // smallest natural number (i.e. the quantity which symbolically represents the detection of some phenomenon)
length("XX") = 2 = (1 + 1). // second smallest natural number
length("XXX") = 3 = (2 + 1) = (1 + 2) = ((1 + 1) + 1) = (1 + (1 + 1)). // third smallest natural number
```

INTEGER: an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of each natural number, each natural number multiplied by negative one, and zero.

```/**
* array represents a finite interval of some
* Cartesian grid axis (i.e. the interval whose
* endpoints are -3 and 3) which is partitioned
* into 6 equally-sized subintervals.
*
*                              |
* <-- (-3) -- (-2) -- (-1) -- (0) -- (1) -- (2) -- (3) -->
*                              |
*/
array := [-3, -2, -1, 0, 1, 2, 3]. // absolute_value((-3) - (3)) = absolute_value((3) + (-3)) = absolute_value((-6)) = 6.
subarray_0 := [-3,-2]. // absolute_value((-3) - (-2)) = absolute_value((-3) + (2)) = absolute_value((-1)) = 1.
subarray_1 := [-2, -1]. // absolute_value((-2) - (-1)) = absolute_value((-2) + (1)) = absolute_value((-1)) = 1.
subarray_2 := [-1, 0]. // absolute_value((-1) - (0)) = absolute_value((-1) + (0)) = absolute_value((-1)) = 1.
subarray_3 := [0, 1]. // absolute_value((0) - (1)) = absolute_value((0) + (-1)) = absolute_value((-1)) = 1.
subarray_4 := [1, 2]. // absolute_value((1) - (2)) = absolute_value((1) + (-2)) = absolute_value((-1)) = 1.
subarray_5 := [2, 3]. // absolute_value((2) - (3)) = absolute_value((2) + (-3)) = absolute_value((-1)) = 1.
```

RATIONAL_NUMBER: an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of each integer and each ratio, (A/B), whose numerator is any integer, A, and whose denominator is any nonzero integer, B.

```Let A be any integer.
Let B be any nonzero integer.
By definition, the ratio (A/B) is a rational number.
```
```is_rational_number(1/3) = true.
is_rational_number(1/1) = true.
is_rational_number(square_root(2)) = false.
is_rational_number(square_root(1)) = true. // square_root(1) = 1.
is_rational_number(square_root(0)) = true. // square_root(0) = 0.
is_rational_number(square_root(-1)) = false. // i := square_root(-1). // i is an imaginary number. Each rational number is a real number.
is_rational_number(0/1) = true. // (0/1) = 0.
is_rational_number(0/0) = false. // Infinity is not a number.
is_rational_number(1/0) = false. // Infinity is not a number.
```

IRRATIONAL_NUMBER: an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of real numbers which cannot be represented as a fractions whose numerator is an integer and whose denominator is a nonzero integer.

An example of an irrational number is the golden ratio (i.e. (1 + square_root(2)) / 5).

Another example of an irrational number is Pi (i.e. the radius of a circle divided by its diameter).

REAL_NUMBER an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of numbers which are each not the product of square_root(-1) multiplied by either a rational number or else an irrational number.

IMAGINARY_NUMBER an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of numbers which are each the product of square_root(-1) multiplied by either a rational number or else an irrational number.

```i := square_root(-1). // imaginary number
(i * i) = -1. // real number
((i * i) * i) := ((-1) * i). // imaginary number
```

COMPLEX_NUMBER: the sum of a real number an an imaginary number.

```(2 * i) + 3. // complex number
(2 * i). // imaginary number
(1 * i). // imaginary number
(0 * i) = 0. // real number
```

This web page was last updated on 02_NOVEMBER_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.

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This web page was last updated on 15_NOVEMBER_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.