inverse mapping

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Let f: ST be a bijection, that is, a mapping that is both a one-to-one mapping and an onto mapping. Then a mapping, denoted by f−1, from T to S may be defined as follows: for t in T, f−1(t) is the unique element s of S such that f(s)=t. The mapping f−1: TS, which is also a bijection, is the inverse mapping of f. It has the property that ff−1=iT and f−1f=iS, where iS and iT are the identity mappings on S and T, and ○ denotes composition.

Subjects: Mathematics.

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