A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") iff it is bijective.

Two sets X and Y are called bijective if there is a bijective map from X to Y. In this sense, "bijective" is a synonym for "equipollent" (or "equipotent"). Bijectivity is an equivalence relation on the class of sets.

See also

Bijection, Cardinal Number, Equipollent, Injection, Inverse Function, Surjection

This entry contributed by Margherita Barile

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Barile, Margherita. "Bijective." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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