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

  • range
  • domain

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.
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