inequality

inequality in mathematics, statement that a mathematical expression is less than or greater than some other expression; an inequality is not as specific as an equation , but it does contain information about the expressions involved. The symbols < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) are used in place of the equals sign in expressions of inequalities. As in the case of equations, inequalities can be transformed in various ways. The direction of the inequality remains unchanged if some number is added to both sides or subtracted from both sides or if both sides are multiplied or divided by some positive number; e.g., subtracting 10 from both sides of the inequality x < 8 gives x - 10 < -2, and multiplying the inequality by 2 gives 2 x < 16. Multiplication or division by a negative number reverses the sign of the inequality; e.g., if -2 x < 8, then dividing both sides by -2 results in the inequality x > -4.

inequality A binary relation that typically expresses the relative magnitude of two quantities, usually numbers though more generally elements of a partially ordered set (see partial ordering).

The inequalities defined on the integers usually include

< (less than)

← (less than or equal to)

> (greater than)

≥ (greater than or equal to)

≠ (not equal to)

A similar set of inequalities is usually defined on the real numbers; such inequalities can produce errors when used in programming languages because of the inherent inaccuracies in the way real numbers are usually represented.

The term inequality is often applied to any comparison involving algebraic expressions and using the above symbols. A special case is the triangle inequality: |a + b| ← |a| + |b|

where | | denotes the absolute value function.