from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. Mathematics A function that is onto.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A function of "many-to-one" mapping relationship; more formally, f: X → Y is a surjection if and only if, for every y in the codomain Y, there is at least one x in the domain X with f(x) = y.


sur- + (pro)jection.
(American Heritage® Dictionary of the English Language, Fourth Edition)
This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique. (Wiktionary)


  • '' '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.

    Citizendium, the Citizens' Compendium - Recent changes [en]

  • It is easy to check that this function satisfies the relation, which has to be a surjection since the sequence is strictly increasing..

    Gowers's Weblog

  • But the Zariski topology is not metrizable … is a surjection of sheaves (exercise!), yet the map on global sections is not surjective.

    Secret Blogging Seminar

  • If you think about it, Arrays and Maps share the same underlying formalism (a surjection, not to put too fine a point on it), and in some languages, notably PHP, there isn't a user-visible difference between them.

    Stevey's Blog Rants


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