# Definition:Inequality

## Definition

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

$a < b$
$a \le b$
$a > b$
$a \ge b$

### Strict Inequality

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

That is, an inequality of the form:

$a < b$
$a > b$

### Weak Inequality

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

That is, an inequality of the form:

$a \le b$
$a \ge b$

### Member of Inequality

Let $\RR$ be an inequality.

Let $a \mathrel \RR b$.

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

### Opposite Sense

Two inequalities are of opposite sense if and only if the direction of the ordering which the inequality is different.

That is, whether it is:

a greater than relation: $a > b$

or:

a less than relation: $a < b$

These two are of opposite sense.

## Also defined as

A statement of the form:

$a \ne b$

may or may not be classified as an inequality, depending on the source work inspected.

## Also see

• Results about inequalities can be found here.