Inequality

An inequality is an equation where one side is not necessarily equal, or may not, to the other.

These come in four kinds;

1. An equation which the left hand side is strictly greater than the right denoted $>$
2. An equation which the left hand side is greater than or equal that the right denoted $\geq$
3. An equation which the left hand side is strictly less than the right denoted $<$
4. An equation which the left hand side is greater than or equal that the right denoted $\leq$

For example, 4 is greater than 3, so either;

4>3

3<4

are true statements.

The inequalities are wildly used in more advanced mathematics for example the cosine function is always between -1 and 1 inclusive so you can write;

$-1\leq \cos x\leq 1\;\forall x\in \mathbb {R}$.

This gives the function bounds.

See also

• Equation