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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle <}
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:

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

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

See also