Difference between revisions of "Inequality"
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| − | An inequality is a mathematical expression concerning the relative size of two terms. | + | An '''inequality''' is a mathematical expression concerning the relative size of two terms. |
These come in five kinds; | These come in five kinds; | ||
| − | * An expression in which the left hand side is strictly greater than the right, denoted: <math> | + | * An expression in which the left hand side is strictly greater than the right, denoted: <math>></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 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> | + | * An expression in which the left hand side is strictly less than the right, denoted: <math><</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 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> | * An expression in which the left hand side is not equal to the right, but no further information is implied, denoted: <math>\neq</math> | ||
| Line 16: | Line 16: | ||
are true statements. | 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 | + | 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>. | ||
| − | This gives the function [[bounds]]. | + | This gives the function's [[bounds]]. '<math>\forall x\in\mathbb{R}</math>' means that the preceding inequality is true for all [[Real numbers|real]] values of <math>x</math>. |
==See also== | ==See also== | ||
*[[Equation]] | *[[Equation]] | ||
| − | [[Category: | + | [[Category:Mathematics]] |
Latest revision as of 14:19, July 13, 2016
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: <math>></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><</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;
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:
<math>-1\leq\cos x\leq1\; \forall x\in\mathbb{R}</math>.
This gives the function's bounds. '<math>\forall x\in\mathbb{R}</math>' means that the preceding inequality is true for all real values of <math>x</math>.