Let F: A → B be a one-to-one mapping from set A to set B. If for each element B in B, the original image A of B in A corresponds to it, then the resulting mapping is called the inverse mapping of mapping F: A → B, and it is recorded as 1/f:A→B → A, which must be injective one by one.

There is a mapping f: a->; B, if there is a mapping g: b->; A makes g*f=IA and f*g=IB, where IA and IB are isomorphs on A and B respectively, then G is called the inverse mapping of F. ..

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In many specific mathematical fields, this term is used to describe functions with specific properties associated with this field, such as continuous functions in topology, linear transformations in linear algebra, and so on. In formal logic, this term is sometimes used to represent function predicates, where function is the model of predicates in set theory.

If we extend the two sets in the function definition from non-empty sets to sets of arbitrary elements (not limited to numbers), we can get the concept of mapping: mapping is a term in mathematics that describes a special correspondence between two sets of elements.

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