Inequality - Ordered Sets, Algebra Of Inequalities, Examples

In mathematics, an inequality is a statement about the relative order of members of a set. For instance, if S Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.


is the set of positive integers, and the symbol < is taken to mean less than, then the statement 5 < 6 (read "5 is less than 6") is a true statement about the relative order of 5 and 6 within the set of positive integers. The comparison that is symbolized by < is said to define an ordering relation on the set of positive integers. An inequality is often used for defining a subset of an ordered set. The subset is also the solution set of the inequality.