Words near each other
 ・ Injection fibrosis ・ Injection kicker magnets ・ Injection lipolysis ・ Injection locking ・ Injection mold construction ・ Injection molding machine ・ Injection Molding Magazine ・ Injection molding of liquid silicone rubber ・ Injection moulding ・ Injection port ・ Injection pump ・ Injection seeder ・ Injection site reaction ・ Injection well ・ Injective cogenerator ・ Injective function ・ Injective hull ・ Injective metric space ・ Injective module ・ Injective object ・ Injective sheaf ・ Injector ・ Injector (disambiguation) ・ Injedu ・ Injeh ・ Injeolmi ・ Injera ・ Injevar ・ Injevo ・ Inji
 Dictionary Lists
 mini英和辞書
 mini和英辞書
 Webster 1913
 Latin-English
 FOLDOC
 Wikipedia English
 ウィキペディア
 翻訳と辞書　辞書検索 [ 開発暫定版 ]
 スポンサード リンク
 Injective function ： ウィキペディア英語版
Injective function

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,
: $\forall a,b \in A, \;\; f\left(a\right)=f\left(b\right) \Rightarrow a=b$
which is logically equivalent to the contrapositive,
: $\forall a,b \in A, \;\; a \neq b \Rightarrow f\left(a\right) \neq f\left(b\right)$

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
 翻訳と辞書 : 翻訳のためのインターネットリソース