Number

Natural Numbers (N): The counting numbers starting from 1: N = {1, 2, 3, 4, 5, …}. These are positive integers used for counting.

Whole Numbers (W): Natural numbers together with 0: W = {0, 1, 2, 3, …}. Also called non-negative integers.

Integers (Z): All whole numbers and their negatives: Z = {… , −3, −2, −1, 0, 1, 2, 3, …}. Integers have no fractional or decimal part.

Rational Numbers (Q): Numbers that can be expressed as a fraction \(\tfrac{a}{b}\), where \(a\) and \(b\) are integers and \(b \ne 0\). Rational numbers have either terminating or repeating decimal expansions. Examples: \(\tfrac{1}{5}=0.2,\ \tfrac{2}{3}=0.\overline{6}\).

Irrational Numbers: Numbers that cannot be written as a ratio of two integers. Their decimal expansions are non-terminating and non-repeating. Example: \(\sqrt{2}\), \(\pi\).

Real Numbers (R): All rational and irrational numbers; any number that can be located on the number line.

Complex Numbers (C): Numbers of the form \(a + bi\), where \(a\) and \(b\) are real and \(i\) is the imaginary unit (\(i^2 = -1\)). Real numbers are the special case when \(b = 0\).

Imaginary Numbers: Multiples of \(i\), for example \(2i, -3i\). These do not lie on the real number line but on the imaginary axis in the complex plane.

Even Numbers: Integers divisible by 2 (e.g., 0, 2, 4, 6, …).

Odd Numbers: Integers not divisible by 2 (e.g., 1, 3, 5, 7, …).

Prime Numbers: Integers greater than 1 that have exactly two positive divisors: 1 and themselves. Examples: 2, 3, 5, 7, 11.

Composite Numbers: Integers greater than 1 that have more than two factors (e.g., 4, 6, 8, 9, 10).