Inequality (mathematics)

In contrast to strict inequalities, there are two types of inequality relations that are not strict:

If either of the premises is a strict inequality, then the conclusion is a strict inequality:

In other words, the inequality relation is preserved under addition (or subtraction) and the real numbers are an ordered group under addition.

(this is true because the natural logarithm is a strictly increasing function.)

Mathematicians often use inequalities to bound quantities for which exact formulas cannot be computed easily. Some inequalities are used so often that they have names: