ThmDex – An index of mathematical definitions, results, and conjectures.

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▼	Set of bijections

Definition D1523

Isomorphic sets

Formulation 0

Let $X$ and $Y$ each be a D11: Set such that

(i)	$\text{Iso}(X \to Y)$ is the D2221: Set of bijections from $X$ to $Y$

Then $X$ and $Y$ are isomorphic if and only if \begin{equation} \text{Iso}(X \to Y) \neq \emptyset \end{equation}

Also known as

Equipollent sets, Equipotent sets, Equivalent sets, Equinumerous sets, Bijective sets