View source for Surjective

==English==
{{wikipedia}}

===Pronunciation===
* {{IPA|en|/səˈd͡ʒɛktɪv/|a=RP}}
* {{IPA|en|/sɚˈd͡ʒɛktɪv/|a=GA}}
* {{rhymes|en|ɛktɪv|s=3}}

===Adjective===
{{en-adj|-}}

# {{lb|en|mathematics}} Of, relating to, or being a [[surjection]].
#* '''1974''', Thomas W. Hungerford, ''Algebra'', Springer, [https://books.google.com.au/books?id=t6N_tOQhafoC&pg=PA5&dq=%22surjective%22&hl=en&sa=X&ved=0ahUKEwj-gcT-pLvZAhUMbawKHedQDqAQ6AEIXjAJ#v=onepage&q=%22surjective%22&f=false page 5],
#*: A function <math>\textstyle f</math> is '''surjective''' (or '''onto''') provided <math>\textstyle f(A) = B</math>; in other words,
#*:: for each <math>\textstyle b \in B, b = f(a)</math> for some <math>\textstyle a\in A</math>.
#*: A function <math>\textstyle f</math> is said to be '''bijective''' (or a '''bijection''' or a '''one-to-one correspondence''') if it is both injective and '''surjective'''.
#* {{quote-book|en|year=2010|author=Tullio Ceccherini-Silberstein; Michel Coornaert|title=Cellular Automata and Groups|pageurl=https://books.google.com.au/books?id=N-LSFFaHTKwC&pg=PA133&dq=%22surjective%22&hl=en&sa=X&ved=0ahUKEwj-gcT-pLvZAhUMbawKHedQDqAQ6AEIlQEwEw#v=onepage&q=%22surjective%22&f=false|page=133|publisher=Springer
|passage=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 <math>\textstyle F_2</math>.}}
#* {{quote-book|en|year=2011|author=Ethan D. Bloch|title=Proofs and Fundamentals: A First Course in Abstract Mathematics|edition=2nd|pageurl=https://books.google.com.au/books?id=QJ_537n8zKYC&pg=PA156&dq=%22surjective%22&hl=en&sa=X&ved=0ahUKEwj-gcT-pLvZAhUMbawKHedQDqAQ6AEIbzAM#v=onepage&q=%22surjective%22&f=false|page=156|publisher=Springer
|passage=This function is '''surjective''' and injective, and hence bijective.}}
#: {{syn|en|onto}}

====Derived terms====
{{col2|en
|surjective function
|surjective map}}

====Related terms====
{{col2|en
|surjection
|surjectivity}}

====Translations====
{{trans-top|of, relating, or being a surjection}}
* Catalan: {{t|ca|suprajectiu}}
* Chinese:
*: Mandarin: {{t|cmn|满射的|tr=mǎnshède}}
* Czech: {{t|cs|surjektivní}}
* Danish: {{t|da|surjektiv}}
* Dutch: {{t|nl|surjectief}}
* Finnish: {{t+|fi|surjektiivinen}}
* French: {{t+|fr|surjectif}}
* German: {{t+|de|surjektiv}}
* Irish: {{t|ga|barrtheilgeach}}
* Japanese: {{t|ja|全射の|tr=ぜんしゃの, zenshano}}
* Norwegian:
*: Bokmål: {{t+|nb|surjektiv}}
*: Nynorsk: {{t+|no|surjektiv}}
* Polish: {{t|pl|suriektywny|m}}, {{t+|pl|na|m|f|n}}
* Portuguese: {{t|pt|sobrejetivo}}
* Romanian: {{t|ro|surjectiv}}
* Russian: {{t+|ru|сюръективный}}
* Spanish: {{t|es|sobreyectivo}}
* Swedish: {{t+|sv|surjektiv}}
{{trans-bottom}}

====See also====
* {{l|en|bijective}}
* {{l|en|injective}}

==French==

===Pronunciation===
* {{fr-IPA}}
* {{homophones|fr|surjectives}}

===Adjective===
{{head|fr|adjective form}}

# {{feminine singular of|fr|surjectif}}