Then any element y in b can find its original image x in B.

Necessity: If the mapping F has an inverse mapping, then there is F (- 1) so that any element X in A can find its pixel Y in B.

That is, f is bijective.

Sufficiency: If F is bijective, then there is an existential mapping G, so that

Any element X in A can be found in B as its pixel Y.

Now it is only necessary to prove that there is an inverse mapping with g as f that satisfies the condition.

G(y)=x，f (x) = y。 available

f[g(y)]=f(x)=y

g[f(x)]=g(y)=x

So g = f (- 1). That is, the adequacy of the certificate.

brief introduction

Mapping or projection is also used to define functions in mathematics and related fields. The function is a mapping from a non-empty number set to a non-empty number set, and it can only be a one-to-one mapping or a many-to-one mapping.

Mapping has many names in different fields, and its essence is the same. Such as functions, operators and so on. What needs to be explained here is that a function is a mapping between two data sets, and other mappings are not functions. One-to-one mapping (bijection) is a special mapping, that is, the only correspondence between two groups of elements, usually one-to-one (one-to-one).