surjection.
A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y.
Meaning & usage
A function for which every element of the codomain is mapped to by some element of the domain; (formally) Any function f:X→Y for which for every y∈Y, there is at least one x∈X such that f(x)=y.
Where this word comes from
From French surjection, introduced by the Bourbaki group in their treatise Éléments de mathématique. Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.