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Restriction (mathematics)
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Restriction (mathematics) : ウィキペディア英語版
Restriction (mathematics)

In mathematics, the restriction of a function ''f'' is a new function ''f''|A obtained by choosing a smaller domain ''A'' for the original function ''f''. The notation f is also used.
==Formal definition==
Let be a function from a set to a set , so that the domain of is in (\mathrm \, f \subseteq E). If a set is a subset of , then the restriction of to is the function〔

: _A \colon A \to F.
Informally, the restriction of to is the same function as , but is only defined on A\cap \mathrm \, f.
If the function is thought of as a relation (x,f(x)) on the Cartesian product E \times F, then the restriction of to can be represented by the graph G(_A) = \, where the pairs (x,f(x)) represent edges in the graph .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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