English Dictionary

surjection

IPA（発音記号）

/sɜː(ɹ).d͡ʒɛk.ʃən/

名詞

(set theory) 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.

日本語の意味

全射：集合論における写像で、定義域の各々の元が写像される先である値域のすべての元に対して、少なくとも1つの元が対応する関数。

To prove that f: A → B is a surjection, we must show that for every element b in B there exists an a in A with f(a) = b.

f: A → B が全射であることを証明するには、B の任意の元 b に対して f(a) = b を満たす A の元 a が存在することを示さなければなりません。

意味（1）

(set theory) 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.

In some special cases, however, the number of surjections A→B can be identified.

surjections （ plural ）