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

• Definition:Usual Ordering

• 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.