In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (See also: equality).
- The notation a < b means that a is less than b.
- The notation a > b means that a is greater than b.
- The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.
In each statement above, 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 statements that are not strict:
- The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b)
- The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not smaller than 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.
- The notation a ≫ b means that a is much greater than b.
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 "unconditional" 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.
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