# Definition:Inequality

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## 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**.

### 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 $\RR$.

## 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