# Difference between revisions of "Domain of definition"

From Encyclopedia of Mathematics

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− | The set on which the function considered is given, that is, the collection | + | The set on which the function considered is given, that is, the collection $X$ of all elements $x$ with each of which the given function $f$ associates an element $y$ of some set $Y$. Thus, if $f:X \to Y$, then $X$ is called the domain of definition of $f$. |

====Comments==== | ====Comments==== | ||

− | The set of values of | + | The set of values of $f$, i.e. $f(X)$ if $X$ denotes the domain of definition, is called the [[Range of values|range of values]] of $f$. |

## Revision as of 01:36, 20 April 2012

*of a function*

The set on which the function considered is given, that is, the collection $X$ of all elements $x$ with each of which the given function $f$ associates an element $y$ of some set $Y$. Thus, if $f:X \to Y$, then $X$ is called the domain of definition of $f$.

#### Comments

The set of values of $f$, i.e. $f(X)$ if $X$ denotes the domain of definition, is called the range of values of $f$.

**How to Cite This Entry:**

Domain of definition.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Domain_of_definition&oldid=13605

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article