NUMBERS


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.