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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 ?
Bijectivity. Adams and Tavares pointed out that if the linear sum of the Boolean function [f.sub.i] of each component of the designed nxn S-box was [2.sup.n-1], f was then abijection [44].
Since n|T(k) implies n [less than or equal to] T(k), so log n [less than or equal to] log T(k) < f(k), and the function f being strictly increasing and continuous, by the bijectivity of f, the left side of (26) follows.
Note that the conjectured bijectivity of [sw.sub.r,s] on the domain Dwordr, ([N.sub.a][E.sub.b]) would imply the weaker univariate symmetry property [C.sub.r,s,a,b](q, 1) = [C.sub.r,s,a,b](1, q).
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.