injective

(adjective)

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

Related Terms

Examples of injective in the following topics:

  • Inverse Functions

    • For this rule to be applicable, for a function whose domain is the set $X$ and whose range is the set $Y$, each element $y \in Y$ must correspond to no more than one $x \in X$; a function $f$ with this property is called one-to-one, or information-preserving, or an injection.
    • Such a function is called non-injective or information-losing.
    • If the domain consists of the non-negative numbers, then the function is injective and invertible.

  • Inverse Functions

    • For this rule to be applicable, each element $y \in Y$ must correspond to no more than one $x \in X$; a function $f$ with this property is called one-to-one, information-preserving, or an injection.