different between surjective vs submersion

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

English

Etymology

Borrowed from Latin summersio, summersionem.

Noun

submersion (countable and uncountable, plural submersions)

1. The act of submerging, or the state of being submerged; immersion
2. (mathematics) A differentiable map whose differential is everywhere surjective.

Related terms

• submerse
• submersible
• submerge
• submersive

Translations

French

Etymology

Borrowed from Latin summersio, summersionem.

Noun

submersion f (plural submersions)

1. submersion

Related terms

• submersible
• submerger