surjectiveとは 意味・読み方・使い方

発音

• (Received Pronunciation) IPA: /səˈd͡ʒɛktɪv/
• (General American) IPA: /sɚˈd͡ʒɛktɪv/
• 韻: -ɛktɪv

形容詞

surjective (not comparable)

1. (mathematics) Of, relating to, or being a surjection.
   • 1974, Thomas W. Hungerford, Algebra, Springer, page 5,

     A function ${\displaystyle \textstyle f}$ is surjective (or onto) provided ${\displaystyle \textstyle f(A)=B}$; in other words,

     for each ${\displaystyle \textstyle b\in B,b=f(a)}$ for some ${\displaystyle \textstyle a\in A}$.

     A function ${\displaystyle \textstyle f}$ is said to be bijective (or a bijection or a one-to-one correspondence) if it is both injective and surjective.

   • 2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, Springer, page 133:

     The Garden of Eden Theorem (Theorem 5.3.1) implies that every surjective cellular automaton with finite alphabet over an amenable group is necessarily pre-injective. In this section, we give an example of a surjective but not pre-injective cellular automaton with finite alphabet over the free group ${\displaystyle \textstyle F_{2}}$.

   • 2011, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd edition, Springer, page 156:

     This function is surjective and injective, and hence bijective.

   Synonym: onto

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