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.
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