# NUMBERS_COPY

NUMBERS_COPY

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NUMBERS

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: continuously incrementing an integer variable by exactly one without ever becoming depleted of computational resources (i.e. processing time, memory space, and energy required to perform each addition of one to the sum of all previous additions); the division of a number by zero (which is the process of rendering some definite quantity indefinite by compartmentalizing that definite quantity into indefinitely many partitions).

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 24_JULY_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 09_SEPTEMBER_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.