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.
|a + b| ≤ |a| + |b|