# Bijection

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It has the useful property that for $f:X\rightarrow Y$ that $f^{-1}(y)$ is always defined, and is at most one element.
Thus $f^{-1}$ behaves as a normal function (rather than the always-valid but less useful $f^{-1}:Y\rightarrow\mathcal{P}(X)$ where $\mathcal{P}(X)$ denotes the power set of $X$)