Real Numbers — O/L Mathematics

Real numbers form the foundation of all quantitative mathematics at the O/L level. A real number is any number that can be represented on an infinite number line. This includes all rational numbers and all irrational numbers.

Rational Numbers are numbers that can be expressed as a fraction p/q where p and q are integers and q is not zero. When written as decimals, rational numbers either terminate (like 1/4 = 0.25) or repeat a pattern (like 1/3 = 0.333...). Examples: 2, -5, 3/4, 0.7, 2.333..., 0.142857142857...

Irrational Numbers are numbers that cannot be expressed as a fraction of integers. Their decimal expansions never terminate and never repeat a fixed pattern. Examples: sqrt(2), sqrt(3), pi, e. Note that sqrt(4) = 2 is rational, but sqrt(2) is irrational.

Integers are whole numbers that can be positive, negative, or zero: ..., -3, -2, -1, 0, 1, 2, 3, ...

Natural Numbers are positive integers: 1, 2, 3, 4, ...

Whole Numbers are natural numbers plus zero: 0, 1, 2, 3, ...