If the sense of the inequality is the same for all values of the variables for which its members are defined, then the inequality is called an "absolute" or "unconditonal" inequality. If the sense of an inequality holds only for certain values of the variables involved, but is reversed or destroyed for other values of the variables, it is called a conditional inequality. The sense of an inequality is not changed if both sides are increased or decreased by the same number, or if both sides are multiplied or divided by a positive number; the sense of an inequality is reversed if both members are multiplied or divided by a negative number.
Inequalities are governed by the following properties:
The Trichotomy Property The trichotomy property states:
The Addition and Subtraction Properties of Inequalities The properties which deal with addition and subtraction states:
The Multiplication and Division Properties of Inequalities The properties which deal with multiplication and division state:
See also Binary relation, partially ordered set, inequation
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