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In mathematics, a function ''f'' from a set ''X'' to a set ''Y'' is surjective (or onto), or a surjection, if every element ''y'' in ''Y'' has a corresponding element ''x'' in ''X'' such that ''f''(''x'') = ''y''. The function ''f'' may map more than one element of ''X'' to the same element of ''Y''. The term ''surjective'' and the related terms ''injective'' and ''bijective'' were introduced by Nicolas Bourbaki,〔.〕 the pseudonym for a group of mainly French 20th-century mathematicians who wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French prefix ''sur'' means ''over'' or ''above'' and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. ==Definition== A surjective function is a function whose image is equal to its codomain. Equivalently, a function ''f'' with domain ''X'' and codomain ''Y'' is surjective if for every ''y'' in ''Y'' there exists at least one ''x'' in ''X'' with . Surjections are sometimes denoted by a two-headed rightwards arrow (),〔(【引用サイトリンク】 url = http://www.unicode.org/charts/PDF/U2190.pdf )〕 as in ''f'' : ''X'' ↠ ''Y''. Symbolically, :If , then is said to be surjective if :. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Surjective function」の詳細全文を読む スポンサード リンク
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