ThmDex – An index of mathematical definitions, results, and conjectures.
Result R2599 on D2223: Set of surjections
Cantor's theorem
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathcal{P}(X)$ is the D80: Power set of $X$
(ii) $\text{Sur}(X \to \mathcal{P}(X))$ is the D2223: Set of surjections from $X$ to $\mathcal{P}(X)$
Then \begin{equation} \text{Sur}(X \to \mathcal{P}(X)) = \emptyset \end{equation}