# Definition:Cartesian Product/Family of Sets/Axiom of Choice

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## Definition

It is of the utmost importance that one be aware that for many $I$, establishing non-emptiness of $\ds \prod_{i \mathop \in I} S_i$ requires a suitable version of the Axiom of Choice.

Details on this correspondence can be found on Equivalence of Formulations of Axiom of Choice.

This article, or a section of it, needs explaining.What is meant by "for many $I$"? Clarification needed: which $I$ require which versions? The link cited does not help.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.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 `{{Explain}}` from the code. |