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

Result R4147 on D2758: Cylinder set

Not all subsets of a cartesian product need be cylinder sets

Formulation 0

Let $X : = \{ 0, 1 \}$ be a D11: Set such that

(i)	\begin{equation} Y : = \{ (0, 1), (1, 0) \} \end{equation}

Then

(1)	\begin{equation} Y \subseteq X \times X \end{equation}
(2)	\begin{equation} \forall \, E, F \subseteq X : Y \neq E \times F \end{equation}