Definition:Inequality

Definition

An inequality is a mathematical statement that two expressions relate in one of several conventional ways:

$a < b$

$a \le b$

$a > b$

$a \ge b$

A statement of the form:

$a \ne b$

may or may not be considered an inequality.

A strict inequality is an inequality which does not permit the possibility of equality.

That is, an inequality of the form:

$a < b$

$a > b$

A weak inequality is an inequality which permits the possibility of equality.

That is, an inequality of the form:

$a \le b$

$a \ge b$

Let $\RR$ be an inequality.

Let $a \mathrel \RR b$.

Then both $a$ and $b$ are referred to as members of the inequality $\RR$.