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Classification of Numbers

This classification of Numbers represents the most accepted elementary classification, and is useful in computing sense.

ClassSymbolDescription
Natural NumberNatural numbers are defined as non-negative counting numbers: $Natural Number Symbol$ = { 0, 1, 2, 3, 4, ... }. Some exclude 0 (zero) from the set: $Natural Number Symbol$* = $Natural Number Symbol$\{0} = { 1, 2, 3, 4, ... }.
IntegerIntegers extend $Natural Number Symbol$ by including the negative of counting numbers:
$Integer Symbol$ = { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }.
The symbol $Integer Symbol$ stands for Zahlen, the German word for "numbers".
Rational NumberA rational number is the ratio or quotient of an integer and another non-zero integer:
= {n/m | n, m ∈ $Integer Symbol$, m ≠ 0 }.
E.g.: -100, -20¼, -1.5, 0, 1, 1.5, 1½ 2¾, 1.75, &c
Irrational NumberIrrational numbers are numbers which cannot be represented as fractions.
E.g.: √2, √3;, π, e.
Real NumberReal numbers are all numbers on a number line. The set of is the union of all rational numbers and all irrational numbers.
Imaginary NumberAn imaginary number is a number which square is a negative real number, and is denoted by the symbol i, so that i2 = -1.
E.g.: -5i, 3i, 7.5i, &c.
In some technical applications, j is used as the symbol for imaginary number instead of i.
Complex NumberA complex number consists of two part, real number and imaginary number, and is also expressed in the form a + bi (i is notation for imaginary part of the number).
E.g.: 7 + 2i