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Undid revision 1250997369 by Closed Limelike Curves (talk) this is true of only one of the two bolded phrases, but also (1) it does not require it in the first paragraph, and (2) if in fact if the term is not mentioned anywhere in this article then a more plausible conclusion is that the redirect should not exist |
Partly undid revision 1250999018 by JayBeeEll (talk): unrestricted ___domain redirects to total function, which in turn redirects here; give a chance to supply a citation for it before deleting the former redirect Tag: Reverted |
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{{more footnotes|date=August 2014}}
In [[mathematics]], a '''partial function''' {{mvar|f}} from a [[Set (mathematics)|set]] {{mvar|X}} to a set {{mvar|Y}} is a [[function (mathematics)|function]] from a [[subset]] {{mvar|S}} of {{mvar|X}} (possibly the whole {{mvar|X}} itself) to {{mvar|Y}}. The subset {{mvar|S}}, that is, the ''[[Domain of a function|___domain]]'' of {{mvar|f}} viewed as a function, is called the '''___domain of definition''' or '''natural ___domain''' of {{mvar|f}}. If {{mvar|S}} equals {{mvar|X}}, that is, if {{mvar|f}} is defined on every element in {{mvar|X}}, then {{mvar|f}} is said to be a '''total function''', or to have an '''unrestricted ___domain'''.{{cn|reason=Give a citation for each of the names.}}
More technically, a partial function is a [[binary relation]] over two [[Set (mathematics)|sets]] that associates to every element of the first set ''at most'' one element of the second set; it is thus a [[univalent relation]]. This generalizes the concept of a (total) [[Function (mathematics)|function]] by not requiring ''every'' element of the first set to be associated to an element of the second set.
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