Surjective function: Difference between revisions
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In [[mathematics]], a '''surjective function''' or '''onto function''' or '''surjection''' is a [[function (mathematics)|function]] for which every possible output value occurs for one or more input values: that is, its image is the whole of its codomain. | In [[mathematics]], a '''surjective function''' or '''onto function''' or '''surjection''' is a [[function (mathematics)|function]] for which every possible output value occurs for one or more input values: that is, its image is the whole of its codomain. | ||
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* [[Bijective function]] | * [[Bijective function]] | ||
* [[Injective function]] | * [[Injective function]] | ||
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Latest revision as of 16:00, 23 October 2024
In mathematics, a surjective function or onto function or surjection is a function for which every possible output value occurs for one or more input values: that is, its image is the whole of its codomain.
An surjective function f has an inverse (this requires us to assume the Axiom of Choice). If y is an element of the image set of f, then there is at least one input x such that . We define to be one of these x values. We have for all y in the codomain.
