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

Result R3931 on D70: Set difference

Subtracting set from empty set

Formulation 0

Let $X$ be a D11: Set.

Then \begin{equation} \emptyset \setminus X = \emptyset \end{equation}

Formulation 1

Let $X$ be a D11: Set.

Then \begin{equation} X^{\complement_{\emptyset}} = \emptyset \end{equation}

Formulation 2

Let $X$ be a D11: Set.

Then \begin{equation} \complement_{\emptyset} X = \emptyset \end{equation}