Definition:Injection

Also known as
Authors who prefer to limit the jargon of mathematics tend to use the term one-one (or 1-1) or one-to-one for injective, and one-one mapping or one-to-one mapping for injection.

However, because of the possible confusion with the term one-to-one correspondence, it is recommended that the rather more technical-sounding term injection is used instead.

An injective mapping is sometimes written $f: S \rightarrowtail T$ or $f: S \hookrightarrow T$.

Also see

 * Definition:Surjection
 * Definition:Bijection


 * In Injection iff Left Cancellable it is shown that a mapping $f$ is an injection iff it is left cancellable.


 * In Injection iff Inverse of Image is Mapping it is shown that a mapping $f$ is an injection iff the inverse of $f$ from its image is itself a mapping.


 * In Injection iff Left Inverse it is shown that a mapping $f$ is an injection iff it has a left inverse.


 * In Preimages all Singletons iff Injection, it is shown that a mapping $f$ is an injection iff the preimage of every element of the codomain is guaranteed to have no more than one element.


 * In Subset equals Preimage of Image iff Mapping is Injection, it is shown that a mapping $f$ is an injection iff the preimage of the image of every subset of its domain equals that subset.