surjective

English

English Wikipedia has an article on:

surjective

Wikipedia

Pronunciation

• (Received Pronunciation) IPA^(key): /səˈd͡ʒɛktɪv/
• (General American) IPA^(key): /sɚˈd͡ʒɛktɪv/
• Rhymes: -ɛktɪv

Adjective

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

Derived terms

Related terms

Translations

See also

• bijective
• injective

French

Pronunciation

• IPA^(key): /syʁ.ʒɛk.tiv/
• Homophone: surjectives

Adjective

surjective

1. feminine singular of surjectif