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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 ?
We show that [THETA] and [PHI] are mutually inverse bijections. Due to symmetry, it suffices to show that [THETA]([PHI](I)) = I for any I [member of] Id(S).
[P.sub.2]: [F.sup.d.sub.n] is a continuous function, negative, and strictly increasing on the interval [mathematical expression not reproducible] and realizes a bijection on the interval [mathematical expression not reproducible] that is to say, [F.sup.d.sub.n] must have the following: a limit 0 to the point [x.sub.ind]; that is to say, [mathematical expression not reproducible]; a limit -1 to the point []; that is to say, [mathematical expression not reproducible].
This bijection relates each element ([i.sub.0],..., [i.sub.n]) in [N.sup.n+1] by its order i defined in (20).
Let it be a bijection [psi]: P [right arrow] P and an line [??] [member of] L.
I(X) = {f : Dom(f) [[subset].bar] X [right arrow]* Im(f) [[subset].bar] X | f is a bijection }.
One of the main reasons being that they are in bijection with permutations.
The bijection [chi] : [sigma] [right arrow] [([[sigma].sup.c]).sup.r], allows to conclude for [alpha] = 312.
A connected graph G (V , E) is said to be (a, d ) -antimagic if there exist positive integers a, d and a bijection Hollander proved that necessary conditions for Cn P2 to be (a, d ) -antimagic.
We can consider f as a bijection between P(T) and [Z.sub.k], so for every nonzero b [member of] [Z.sub.k], there exists a path with weight b.
Let S is a right normal orthodox semigroup with an inverse transversal S[degrees], Blyth and Almeida Snatos in [4] proved that there is an order-preserving bijection from the set of all locally maximal S[degrees]-cones to the set of all left amenable orders definable on S and the natural partial order is the smallest left amenable partial order(see theorems 7 and 11 in [4]).
Then [[PSI].sub.[Real part]] is bijection fuzzy map, but the converse not necessarily true.
The bijection preserves inclusions and normality, so it is effectively perfect.