\begin{definition}[Definition:Cartesian Product/Uncountable]
Let $I$ be an indexing set with uncountable cardinality.
Let $\family {S_\alpha}_{\alpha \mathop \in I}$ be a family of sets indexed by $I$.
The '''cartesian product''' of $\family {S_\alpha}$ is denoted:
:$\ds \prod_{\alpha \mathop \in I} S_\alpha$
{{DefinitionWanted|Yes, it is clear this does not precisely define this entity. Should really reference Definition:Cartesian Product of Family but having trouble getting my head round it.}}
{{LinkToCategory|Cartesian Product|Cartesian products}}
{{NamedforDef|René Descartes}}
Category:Definitions/Cartesian Product
\end{definition}