bijection

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Related to Bijective function: inverse function, Injective function

bijection

[′bī‚jek·shən]
(mathematics)
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.

bijection

(mathematics)
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 ?
(3) Let [v.sub.n] : [P.sub.n] [right arrow] [Z.sub.N(n)] be a bijective function such that
Let [phi] : X [right arrow] Y be a bijective function and (B, [B.sup.*]) be an (L,M)-dffb on Y.
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.
Let w(x) : [bar.[OMEGA]] [right arrow] [bar.[OMEGA]] be a bijective function in [C.sup.3] with w'(x) > 0 for all x and let [w.sub.i] be the set of collocation points.
Since [psi] is a bijective function, we say that sq is the status quo of the municipal political system and S is the policy space (Figure 1).
The evidence-corresponding-relations defined by a bijective function can describe the equivalent relations of traders' evidences and give a method to determine whether someone has forged evidences in transaction.
From (5.4) and from the fact that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a bijective function, it derives that v is an extremum point (respectively minimum, maximum) for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] if and only if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is an extremum point (respectively minimum, maximum) for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
This defines the bijective function discretePolyg(r) that returns the corresponding element from I.
A bijective function h : [V.sub.1] [right arrow] [V.sub.2] is called an m-polar morphism or m-polar h-morphism if there exists two numbers [l.sub.1] > 0 and [l.sub.2] > 0 such that [p.sub.i] [omicron] [W.sub.2](h(u)) = [l.sub.1][p.sub.i] [omicron] [W.sub.1](u), [for all]u [member of] [V.sub.1], [p.sub.i] [omicron] [F.sub.2](h(u)h(v)) = [l.sub.2][p.sub.i] [omicron] [F.sub.1](uv), [for all]uv [member of] [E.sub.1], i = 1, 2, ..., m.
A graph G is a super edge-magic graph if and only if there exists a bijective function f : V(G) [right arrow] {1, 2, ..., v} such that the set S = {f(x) + f(y) : xy [member of] E(G)} consists of e consecutive integers.
Let h : Vi [right arrow] V2 be an isomorphism of G1 onto G2 then h is bijective function. Therefore h(xi) = x2, for all x1 [member of] V
Define [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and let f be a bijective function from the set W to the set [N.sub.|W| + 1] {1}.