# Definition:Cartesian Product/Uncountable

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## 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.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. |

- Results about
**Cartesian products**can be found here.

## Source of Name

This entry was named for RenĂ© Descartes.