
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 nonnegative 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 nonzero 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 i^{2} = 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 

