Interactive Real Analysis - part of MathCS.org

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A function f from A to B is called one to one (or one-one) if whenever f(a) = f(b) then a = b. Such functions are also called injections.

A function f from A to B is called onto if for all b in B there is an a in A such that f(a) = b. Such functions are also called surjections.

A function f from A to B is called a bijection if it is one to one and onto, i.e. bijections are functions that are injective and surjective.

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