injective
Adjective
Meaning
injective (not comparable)
(mathematics) of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic
Synonym: one-to-one
Related terms
Phrases with the word
Examples
A bilipschitz function is the same thing as an injective Lipschitz function whose inverse function is also Lipschitz.
A function f with a left inverse is necessarily injective.
A parameterization is generally required to have distinct parameter values give rise to distinct distributions, i.e. must hold (in other words, it must be injective ).
An embedding, or a smooth embedding, is defined to be an injective immersion which is an embedding in the topological sense mentioned above (i.e. homeomorphism onto its image).
Algebra In general, for an algebraic category C, an embedding between two C-algebraic structures X and Y is a C-morphism e:X→Y which is injective.
A function f that is not injective is sometimes called many-to-one.