Classification of Numbers

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

Class	Symbol	Description
Natural Number		Natural numbers are defined as non-negative counting numbers: = { 0, 1, 2, 3, 4, ... }. Some exclude 0 (zero) from the set: * = \{0} = { 1, 2, 3, 4, ... }.
Integer		Integers extend by including the negative of counting numbers: = { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }. The symbol stands for Zahlen, the German word for "numbers".
Rational Number		A rational number is the ratio or quotient of an integer and another non-zero integer: = {n/m | n, m ∈ , m ≠ 0 }. E.g.: -100, -20¼, -1.5, 0, 1, 1.5, 1½ 2¾, 1.75, &c
Irrational Number		Irrational numbers are numbers which cannot be represented as fractions. E.g.: √2, √3;, π, e.
Real Number		Real numbers are all numbers on a number line. The set of is the union of all rational numbers and all irrational numbers.
Imaginary Number		An 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 Number		A 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