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Difference between revisions of "Domain of definition"

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''of a function''
 
''of a function''
  
The set on which the function considered is given, that is, the collection <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337801.png" /> of all elements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337802.png" /> with each of which the given function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337803.png" /> associates an element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337804.png" /> of some set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337805.png" />. Thus, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337806.png" />, then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337807.png" /> is called the domain of definition of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337808.png" />.
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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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d0337809.png" />, i.e. <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d03378010.png" /> if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d03378011.png" /> denotes the domain of definition, is called the [[Range of values|range of values]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033780/d03378012.png" />.
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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 $f$.

Latest revision as of 06:56, 25 December 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