chapter  4
Inequalities
Pages 6

An inequality is a statement about real numbers involving one of the symbols“>,” “≥,” “<” or “≤”; for example, x > 2 or x2−4y≤ 2x + 2. In this chapterwe shall present some elementary notions concerning manipulation of inequal-ities.Recall from Chapter 2 the basic Rules 2.1 satisfied by addition and multipli-cation of real numbers. As we mentioned there, there are various further rulesconcerning the ordering of the real numbers. Here they are: RULES 4.1 (1) If x ∈ R, then either x > 0 or x < 0 or x = 0 (and just one of these

is true).