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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


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.
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References in periodicals archive ?
If [phi] is a refined neutrosophic bijective homomorphism then it is called refined neutrosophic isomorphism and we write RNQ(H) = RNQ(J).
Moreover, X denotes AddRoundKey, and S represents the bijective nonlinear mapping, i.e., S(a) = S([a.sub.15] [parallel] [a.sub.14] [parallel] [a.sub.13] *** [parallel] [a.sub.2] [parallel] [a.sub.1] [parallel] [a.sub.0]) = [b.sub.15] [parallel] [b.sub.14] [parallel] [b.sub.13] *** [parallel] [b.sub.2] [parallel] [b.sub.1] [parallel] [b.sub.0], where [b.sub.i] = [pi]([a.sub.i])(0 < i < 15).
Let [phi] : X [right arrow] Y be a bijective function and (B, [B.sup.*]) be an (L,M)-dffb on Y.
Then by the same discussion as the proof of Proposition 15 in Case 1, we have [S.sup.r]([rho]) = [S.sup.r]([phi]([rho])), [phi]([P.sub.1](H)) = [P.sub.1](H), and that [phi] is a bijective map which preserves orthogonality in both directions.
(3) Let [v.sub.n] : [P.sub.n] [right arrow] [Z.sub.N(n)] be a bijective function such that
Yu, "Efficient unicast in bijective connection networks with the restricted faulty node set," Information Sciences, vol.
Indeed, it is easy to see that the family of bijective linear functions [R.sup.m] [right arrow] [R.sup.m] is l-lineable if and only if there are bijective linear functions [f.sub.1],..., [f.sub.l] : [R.sup.m] [right arrow] [R.sup.m] such that, for every x [member of] [R.sup.m] \ {0}, the set {[f.sub.1](x),..., [f.sub.l](x)} is a linearly independent system.
A fuzzy graph (Eq.) is knows as a fuzzy magic graph if there exist two bijective functions (Eq.) and (Eq.) ]such that (Eq.) and (Eq.) for all (Eq.) where (Eq.) is a fuzzy magic constant.