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A mapping ƒ from a set A onto a set B which is both an injection and a surjection; that is, for every element b of B there is a unique element a of A for which ƒ (a) = b. Also known as bijective mapping.


A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain.

For a general bijection f from the set A to the set B:

f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.

A and B could be disjoint sets.

See also injection, surjection, isomorphism, permutation.
References in periodicals archive ?
The isomorphism classes of ample division algebras in C(G,[omega], k) are in 1-1 correspondence with the good triples (D, [phi], [sigma]) where D represents an iso-class of associative division k-algebras, [phi] : G [right arrow] Aut(D) represents a conjugacy class in C(G,Out(D)), and [sigma] : G x G [right arrow] [D.
From Difficult to Easy" From Easy to Difficult" Stage I: The Target Task Stage I: The Anchoring Task Encouraging Encouraging "Part-Whole" Ideas 1-1 Correspondence Task 1-4: The horizontal Task 1: The geometric representation representation Task 2: The explicit representation Stage II: The Anchoring Task Stage II: The Bridging Tasks Encouraging 1-1 Correspondence Tasks 1-2: The vertical representation Tasks 1-3: The geometric Stage III: The Target Task representation Task 1: The horizontal representation.
By Cantor's theorem, there should be more classes of entities than there are entities; hence, if one can find a 1-1 correspondence between some entities and all classes of entities, Cantorian reasoning will lead to a contradiction.