Standard Lemma guide

surjection

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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  • /sɜː(ɹ)ˈd͡ʒɛk.ʃən/
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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, set-theory

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique. Ultimately borrowed from Latin superiectiō (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).

Across languages

Translations

25 source translations are retained for this English entry.

  • Bulgarian: сюрекция (sjurekcija) — function that is a many-to-one mapping
  • Catalan: funció exhaustiva — function that is a many-to-one mapping
  • Chinese Mandarin: 满射 (mǎnshè) — function that is a many-to-one mapping
  • Czech: surjekce — function that is a many-to-one mapping
  • Estonian: sürjektsioon — function that is a many-to-one mapping
  • Estonian: surjection — function that is a many-to-one mapping
  • Finnish: surjektio — function that is a many-to-one mapping
  • French: surjection — function that is a many-to-one mapping
  • German: Surjektion — function that is a many-to-one mapping
  • German: surjektive Funktion — function that is a many-to-one mapping
  • Greek: επίρριψη (epírripsi) — function that is a many-to-one mapping
  • Ido: surjekto — function that is a many-to-one mapping
  • Italian: suriezione — function that is a many-to-one mapping
  • Japanese: 全射 (zensha) — function that is a many-to-one mapping
  • Korean: 전사 (jeonsa) — function that is a many-to-one mapping
  • Polish: suriekcja — function that is a many-to-one mapping
  • Portuguese: sobrejeção — function that is a many-to-one mapping
  • Romanian: surjecție — function that is a many-to-one mapping
  • Romanian: funcție surjectivă — function that is a many-to-one mapping
  • Russian: сюръе́кция (sjurʺjékcija) — function that is a many-to-one mapping
  • Serbo-Croatian: surjekcija — function that is a many-to-one mapping
  • Slovak: surjekcia — function that is a many-to-one mapping
  • Spanish: función sobreyectiva — function that is a many-to-one mapping
  • Swedish: surjektion — function that is a many-to-one mapping
  • Vietnamese: toàn ánh — function that is a many-to-one mapping