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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 ?
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).
Since Ore extensions of bijective type are skew PBW extensions.
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
Bijective mapping between nodes on the receiver end and units on the sender end are applied in interpolation method.
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.
We observe that the function p [fleche diestra] [s.sub.p] from (2/3, 2) into (0,1) is bijective; with this in mind one can combine Szasz's results with our main theorem in order to give p-summability of the periodic Fourier transform on the interval (2/3, ([infinito]).
where U[(H).sub.Q] = {T [member of] U(H) | TQ[T.sup.-1] = Q} is the isotropy group of Q, which is moreover bijective but which is not a homeomorphism.