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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 ?
It is easy to see that for J' [[subset].bar] J, [THETA](J) [[subset].bar] [THETA](J) and the same for [PHI]; thus [THETA] and [PHI] are order-preserving bijections and therefore preserve all meets and joins.
Every bijections of set to points P on yourself to affine plane A = (P, L, I) is a his collineation.
Then the maps [[PHI].sub.n] and [[PSI].sub.n] are bijections.
A partial action [alpha] = ({[X.sub.g]}[g.sub.[member of]G], {[[[alpha].sub.g]}.sub.g[member of]G]) of a group G on a set X consists of a family indexed by G of subsets [X.sub.g] [[subset].bar] X and a family of bijections [[alpha].sub.g] : [X.sub.g-1] [right arrow] [X.sub.g] for each g [G.sub.G], satisfying the following conditions:
Section 3 presents the different bijections we need to relate corners in tree-like tableaux with permutations.
For the sets counted by the Motzkin numbers, we exhibit bijections between them and the set of Motzkin paths.
To hide the encryption key, we must merge several steps of each round function of SHARK into table lookups blended by randomly generated mixing bijections. In this section, we investigate how to design such tables and how randomly generated mixing bijections can be counteracted.
A bijection g:V E F--{1,2,...,p+q+f} is called a labeling of type (1,1,1) and a bijection h:V E {1,2,...,p+q} is called a labeling of type (1,1,0).
The set SSYM([G.sub.H],*) = SSYM([G.sub.H]) of all Smarandache bijections (S-bijections) in [G.sub.H] i.e A [member of] SYM([G.sub.H]) such that A : H [right arrow] H forms a group called the Smarandache permutation (symmetric) group [S- permutation group] of [G.sub.H].
The orbiquotient X[/.sup.orb] G is well defined up to canonical bijections. Indeed if h = kg[k.sup.-1] then the map [psi]: [X.sup.g] [right arrow] [X.sup.h] given by [psi](x) = kx induces a bijection
What is more the wavefunctions were "traced" in time in order for one to prove possible bijections. Surprisingly Unruh makes the following claim:
Moreover, there is only one interval-preserving bijection (namely transposition), compared to an indefinitely large number of bijections (of which inversion is one) that do not preserve intervals.