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bijection
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Definition/Summary
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A function f: A [itex]\rightarrow[/itex] B is a bijection if for every b [itex]\in[/itex] B there is exactly one x [itex]\in[/itex] A such that f(x) = b.
The inverse of a bijection f: A [itex]\rightarrow[/itex] B is the function g: B [itex]\rightarrow[/itex] A such that, for each b [itex]\in[/itex] B, g(b) is the unique element x [itex]\in[/itex] A such that f(x)= b. We write f[itex]^{-1}[/itex] for the function g.
The inverse f[itex]^{-1}[/itex] of a bijection f is also a bijection, and its inverse is f. In other words: (f[itex]^{-1}[/itex])[itex]^{-1}[/itex] = f.
A function is bijective if and only it is both an injection and a surjection. |
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Recent forum threads on bijection
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Breakdown
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Mathematics
> Foundations
>> Set Theory
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Commentary
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