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| | Hi there, I am Alyson Pomerleau and I think it sounds fairly good when you say it. My wife and I live in Kentucky. I am presently a journey agent. To perform lacross is some thing he would never give up.<br><br>Feel free to visit my homepage: [http://www.telefonsakalari.net/profile.php?u=AnFetherst psychic phone] |
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| | image1 = Injection keine Injektion 2a.svg
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| | caption1 = This diagram represents a single-valued function with domain <math>\{ 1, 2, 3 \}</math>. Each input, on the left, maps to a single output, on the right. This function is not [[injective]], however, because two different numbers both map to the output "C"
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| | image2 = Injection keine Injektion 1.svg
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| | caption2 = This does ''not'' represent a single-valued function; the input "2" maps to two distinct outputs. This type of correspondence is a [[multi-valued function]].
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| A '''single-valued function''' is an emphatic term for a [[mathematical function]] in the usual sense. That is, each element of the [[function domain|function's domain]] maps to a single, well-defined element of its range. This contrasts with a general [[binary relation]], which can be viewed as being a [[multi-valued function]].
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| == Example ==
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| In [[complex analysis]], each complex number other than 0 has three distinct cube roots. Therefore, the function ''f''(''z'') = ''z''<sup>1/3</sup> can be naturally treated as a multi-valued function in which each number other than zero maps to three distinct values. The theory of [[Riemann surfaces]] gives a way to study the behavior of this function and other multi-valued functions on the complex numbers.
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| == Injective functions ==
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| A function is [[injective function|injective]] (also called "one-to-one") if each element of the range arises from a single element of the domain. In contrast, a function is single-valued if each element of the domain maps to a single element of the domain.
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| [[Category:Mathematical terminology]]
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| [[Category:Types of functions]]
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Latest revision as of 20:19, 10 December 2014
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