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bijection

双向单射; 双单射

The Free On-line Dictionary of Computing (foldoc)

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}.

(2001-05-10)

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bijection	查看　bijection　在百度字典中的解释	百度英翻中〔查看〕
bijection	查看　bijection　在Google字典中的解释	Google英翻中〔查看〕
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英文字典中文字典相关资料:

How to define a bijection between $(0,1)$ and $(0,1]$?
If A is a countable infinite set and a is any element in A, then: there's a bijection for A \ {a} and A; Or, equivalently if A is contained strictly in B, b is in B \ A, A is countably infinite then: there's a bijection for A $\bigcup$ {b} and A;
is there a bijection for $f: \\mathbb R \\to \\mathbb C$?
If you just want a bijection as sets, the answer is yes That’s exactly what it means for two sets to have the same cardinality If you’re looking for a bijection that preserves some structure, that will depend on precisely what you’re trying to preserve but the answer is very probably no
elementary set theory - Bijection and Uncountable Sets (understanding . . .
we can find a bijection between any two countable sets (I think this is correct) No For example, some countable sets are countably infinite while others are finite However, there is a bijection between any two countably infinite sets If we find a bijection between two finite sets, then the two sets must be of the same cardinality Yes
functions - Notation for bijection - Mathematics Stack Exchange
That is, given $\sigma\in S_3$ we get a bijection $\alpha\circ\sigma\circ\chi^{-1}\colon X\to A$ and any bijection can be produced in such a way Now take your favourite notation for peremutations Share
Bijective vs Isomorphism - Mathematics Stack Exchange
A bijection is an isomorphism in the category of Sets When the word "isomorphism" is used, it is always referred to the category you are working in I will list some categories including their typical names for isomorphism: Sets: Bijection; Groups: Isomorphism; Top: Homeomorphism; Differentiable Manifolds: Diffeomorphism; Riemannian Manifolds

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