Surjective function: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch m (typo) |
imported>Richard Pinch (subpages) |
||
| Line 1: | Line 1: | ||
{{subpages}} | |||
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. | ||
Revision as of 12:08, 13 November 2008
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.
