Multivalued function: Difference between revisions

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In [[mathematics]], a '''multivalued function''' (short form: '''multifunction'''; other names: '''many-valued function''', '''set-valued function''', '''set-valued map''', '''multi-valued map''', '''multimap''', '''correspondence''', '''carrier''') is a [[binary relation|left-total relation]]; that is, every [[Input/output|input]] is associated with at least one [[output]].

In the strict sencesense, a "well-defined" [[function (mathematics)|function]] associates one, and only one, output to any particular input. The term "multivalued function" is, therefore, a [[misnomer]] because functions are single-valued. Multivalued functions often arise as inverses of functions that are not [[injective]]. Such functions do not have an [[inverse function]], but they do have an [[inverse relation]]. The multivalued function corresponds to this inverse relation.

==Examples==