Inequality

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An inequality is a mathematical expression concerning the relative size of two terms.

These come in five kinds;

  • An expression in which the left hand side is strictly greater than the right, denoted: >
  • An expression in which the left hand side is greater than or equal than the right, denoted: \geq
  • An expression in which the left hand side is strictly less than the right, denoted: <
  • An expression in which the left hand side is greater than or equal than the right, denoted: \leq
  • An expression in which the left hand side is not equal to the right, but no further information is implied, denoted: \neq

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

4>3

3<4

are true statements.

The inequalities are widely 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\leq1\; \forall x\in\mathbb{R}.

This gives the function's bounds. '\forall x\in\mathbb{R}' means that the preceding inequality is true for all real values of x.

See also

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