Every bijection yields an inverse function

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Let [ilmath]X[/ilmath] and [ilmath]Y[/ilmath] be sets and suppose [ilmath]f:X\rightarrow Y[/ilmath] is a map between them, and that it is a bijective map. Then there exists a unique function:

  • [ilmath]f^{-1}:Y\rightarrow X[/ilmath] such that [ilmath]f^{-1}(y)=x\iff f(x)=y[/ilmath]


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