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Related to Bijectivity: Bijective function


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 ?
In [9] the bijectivity of G was proved for m = kn [+ or -] 1.
All this by the commutativity of the shift and its bijectivity.
We see that injectivity, bijectivity and reversibility are equivalent concepts on cellular automata, and they imply surjectivity which is equivalent to pre-injectivity.