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surjective
This term is used exclusively within the specialized register of mathematics, specifically in set theory and topology. It describes a specific property of a function where the range is equal to the codomain, meaning no element in the target set is left unpaired. It is often used interchangeably with the term "onto" in introductory textbooks, though "surjective" is preferred in formal academic and research contexts.
Because it is a technical descriptor of a mathematical mapping, it does not have a metaphorical or casual application in general English. It is typically paired with "injective" (one-to-one) and "bijective" (both injective and surjective) to categorize the nature of a function's mapping.
Meanings
Examples
A function is surjective if its range is equal to its codomain.
Is this mapping surjective or just injective?
The professor explained why the linear transformation was not surjective.
I need to prove that the function is surjective to show it has a right inverse.
The map from the set of integers to the set of parity values is surjective.
Wait, if the function is both injective and surjective, then it must be bijective.
The projection map from a product space to one of its factors is always surjective.
He wondered if there existed a surjective morphism between these two algebraic structures.