different between injective vs surjective

English

Etymology

(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “cf. discussion page”)This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.

Pronunciation

• IPA^(key): /?n?d??kt?v/
• Rhymes: -?kt?v

Adjective

injective (not comparable)

1. (mathematics) of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic

   Synonym: one-to-one

Derived terms

Related terms

• injectively

Translations

French

Pronunciation

• IPA^(key): /??.??k.tiv/
• Homophone: injectives

Adjective

injective

1. feminine singular of injectif

English

Pronunciation

• Rhymes: -?kt?v

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, Springer, 2nd Edition, 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): /sy?.??k.tiv/
• Homophone: surjectives

Adjective

surjective

1. feminine singular of surjectif