surjective
|sur-jec-tive|
🇺🇸
/sɚˈdʒɛktɪv/
🇬🇧
/səˈdʒɛktɪv/
maps onto whole codomain
Etymology
'surjective' originates from French, specifically the word 'surjectif', formed from the prefix 'sur-' (meaning 'over' or 'above' in French) and the Latin root 'jact-'/'ject-' from 'jacere' meaning 'to throw'.
'surjective' was coined in modern mathematical usage (via French 'surjectif') in the 20th century as a counterpart to terms like 'injective' and 'projective', and was adopted into English mathematical vocabulary as 'surjective'.
Component parts originally meant 'over' + 'to throw'; over time the combined term developed a specialized mathematical meaning: 'onto' (a function that reaches every element of its codomain).
Meanings by Part of Speech
Noun 1
a surjective mapping; a function that is surjective (a mapping that is onto its codomain).
This mapping is a surjection from A onto B.
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Noun 2
surjectivity: the property or quality of being surjective.
Surjectivity of a function means every element of the codomain has a preimage.
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Adjective 1
(Mathematics) Of a function: mapping every element of the codomain to at least one element of the domain; equivalent to 'onto'.
The function f: R → R given by f(x)=2x is surjective onto R.
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Last updated: 2025/10/13 15:47