surjective

English

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

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

     A function $\textstyle f$ 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 $\textstyle F_{2}$.

   • 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

• surjective function
• surjective map

 

Related terms

• surjection
• surjectivity

 

Translations

of, relating, or being a surjection

• Catalan: suprajectiu
• Chinese:

  Mandarin: 满射的 (mǎnshède)

• Czech: surjektivní
• Danish: surjektiv
• Dutch: surjectief
• Finnish: surjektiivinen (fi)
• French: surjectif (fr)
• German: surjektiv (de)
• Irish: barrtheilgeach
• Japanese: 全射の (ぜんしゃの, zenshano)
• Norwegian:

  Bokmål: surjektiv (no)

  Nynorsk: surjektiv (no)

• Polish: suriektywny m, na (pl) m or f or n
• Portuguese: sobrejetivo
• Romanian: surjectiv
• Russian: сюръективный (ru) (sjurʺjektivnyj)
• Spanish: sobreyectivo
• Swedish: surjektiv (sv)

See also

• bijective
• injective

French

Pronunciation

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

Adjective

surjective

1. feminine singular of surjectif