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In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of ''at most'' one element of its domain. The term ''one-to-one function'' must not be confused with ''one-to-one correspondence'' (aka bijective function), which uniquely maps all elements in both domain and codomain to each other, (see figures). Occasionally, an injective function from ''X'' to ''Y'' is denoted , using an arrow with a barbed tail ().〔(【引用サイトリンク】 url = http://www.unicode.org/charts/PDF/U2190.pdf )〕 The set of injective functions from ''X'' to ''Y'' may be denoted ''Y''''X'' using a notation derived from that used for falling factorial powers, since if ''X'' and ''Y'' are finite sets with respectively ''m'' and ''n'' elements, the number of injections from ''X'' to ''Y'' is ''n''''m'' (see the twelvefold way). A function ''f'' that is not injective is sometimes called many-to-one. However, this terminology is also sometimes used to mean "single-valued", i.e., each argument is mapped to at most one value. A monomorphism is a generalization of an injective function in category theory. == Definition == Let ''f'' be a function whose domain is a set ''A''. The function ''f'' is injective if and only if for all ''a'' and ''b'' in ''A'', if ''f''(''a'') = ''f''(''b''), then ''a'' = ''b''; that is, ''f''(''a'') = ''f''(''b'') implies ''a'' = ''b''. Equivalently, if ''a'' ≠ ''b'', then ''f''(''a'') ≠ ''f''(''b''). Symbolically, : which is logically equivalent to the contrapositive, : 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「injective function」の詳細全文を読む スポンサード リンク
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