# bijection

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## bijection

[′bī‚jek·shən] (mathematics)

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.## bijection

(mathematics)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.

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.

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