Definition:Cartesian Product/Uncountable

Definition

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:

$\ds \prod_{\alpha \mathop \in I} S_\alpha$

This definition needs to be completed. In particular: 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. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding or completing the definition. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{DefinitionWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Results about Cartesian products can be found here.

Source of Name

This entry was named for René Descartes.