# 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:

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**.

## Sources

- 1972: Murray R. Spiegel and R.W. Boxer:
*Theory and Problems of Statistics*(SI ed.) ... (previous) ... (next): Chapter $1$: Inequalities - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**inequality** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**inequality**:**2.**