**NUMBERS**

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The following terms and their respective definitions describe all types of numbers (and a **number** is a exactly one of limitlessly many unique finite quantities).

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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).

**NUMBER:** a piece of information which represents exactly one finite quantity; a piece of information which can be encoded as a sequence of binary digits (and a binary digit is the smallest unit of information which a computer can verbatim transmit, store, and edit).

**INFINITY:** the instantiation of limitlessly many copies of exactly one pattern; the instantiation of limitlessly many unique patterns.

**NATURAL_NUMBER:** an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of one and of every unique sum comprised of one being added to itself.

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.

**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).

**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 26_NOVEMBER_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.