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injection

Mathematical function that preserves distinctness

EntityQ182003

Also known as one-to-one function · 1-to-1 function · injective function

Subclass of: function
, left-unique relation

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x1 ≠ x2 implies f(x1) ≠ f(x2) (equivalently by contraposition, f(x1) = f(x2) implies x1 = x2). In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain.

Overview

All data

20 statements · 15% with external sources · numbers in brackets are citations

Has characteristic: left-uniqueness
right-uniqueness
left-totality
Different from: surjective function
monomorphism
bijection applies to name of subject: one-to-one function · applies to name of object: one-to-one correspondence
injection
capability to inject

On other databases

11 identifiers linking injection across the web's reference databases

Data quality

statements

15%

externally sourced

Source last edited August 21, 2026. AIDB refreshes this page daily.

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AIDB. (2026). injection (Q182003). Retrieved from https://aidb.si/e/injection-Q182003