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.
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: