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

Result R2833 on D135: Singleton set

Nonempty set is singleton iff all elements equal each other

Formulation 0

Let $X$ be a D11: Set such that

(i)	\begin{equation} X \neq \emptyset \end{equation}

Then $X$ is a D135: Singleton set if and only if \begin{equation} \forall \, x, y \in X : x = y \end{equation}