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Line 1: − + − + − − # An equation which the left hand side is strictly greater than the right denoted <math>></math> − # An equation which the left hand side is greater than or equal that the right denoted <math>\geq</math> − # An equation which the left hand side is strictly less than the right denoted <math><</math> − # An equation which the left hand side is greater than or equal that the right denoted <math>\leq</math> + + + + + Line 16:
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An inequality is an [[equation]] where one side is not necessarily, or may not be, equal to the other.
An inequality is a mathematical expression concerning the relative size of two terms.
These come in four kinds;
These come in five kinds;
* An expression in which the left hand side is strictly greater than the right, denoted: <math>\gt</math>
* An expression in which the left hand side is greater than or equal than the right, denoted: <math>\geq</math>
* An expression in which the left hand side is strictly less than the right, denoted: <math>\lt</math>
* An expression in which the left hand side is greater than or equal than the right, denoted: <math>\leq</math>
* An expression in which the left hand side is not equal to the right, but no further information is implied, denoted: <math>\neq</math>
For example, 4 is greater than 3, so either;
For example, 4 is greater than 3, so either;
are true statements.
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;
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;
<math>-1\leq\cos x\leq1\; \forall x\in\mathbb{R}</math>.
<math>-1\leq\cos x\leq1\; \forall x\in\mathbb{R}</math>.