Inequality (mathematics)

Inequality (mathematics)

In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).

• The notation a ≠ b means that a is not equal to b.

It does not say that one is greater than the other, or even that they can be compared in size.

If the values in question are elements of an ordered set, such as the integers or the real numbers, they can be compared in size.

• The notation a < b means that a is less than b.
• The notation a > b means that a is greater than b.

In either case, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".

In contrast to strict inequalities, there are two types of inequality relations that are not strict:

• The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b, or at most b).
• The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not less than b, or at least b)

An additional use of the notation is to show that one quantity is much greater than another, normally by several orders of magnitude.

• The notation a ≪ b means that a is much less than b. (In measure theory, however, this notation is used for absolute continuity, an unrelated concept.)
• The notation a ≫ b means that a is much greater than b.