# 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 $\displaystyle \prod_{i \mathop \in I} S_i$ requires a suitable version of the Axiom of Choice.

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