# Inequality

An inequality is a mathematical expression concerning the relative size of two terms.

These come in five kinds;

• An expression in which the left hand side is strictly greater than the right, denoted: >
• An expression in which the left hand side is greater than or equal than the right, denoted: $\geq$
• An expression in which the left hand side is strictly less than the right, denoted: <
• An expression in which the left hand side is greater than or equal than the right, denoted: $\leq$
• An expression in which the left hand side is not equal to the right, but no further information is implied, denoted: $\neq$

For example, 4 is greater than 3, so either;

4>3

3<4

are true statements.

The inequalities are widely used in more advanced mathematics for example the cosine function is always between -1 and 1 inclusive so you can write:

$-1\leq\cos x\leq1\; \forall x\in\mathbb{R}$.

This gives the function's bounds. '$\forall x\in\mathbb{R}$' means that the preceding inequality is true for all real values of x.