# Definition talk:Cartesian Product/Family of Sets

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Non-emptiness of this construct is equivalent to the axiom of choice for mappings $S \to I$; there has to come a note mentioning this. --Lord_Farin 15:33, 12 July 2012 (UTC)

- Good call. The page itself is already there - I think we just have to link to it. The source work from which this immediately comes does not mention AoC for another few chapters. The way I understand it is that in order for this definition to make any sense, AoC is necessary (otherwise the ordering tacitly intrinsic to the concept of Cartesian product can not be defined). Sorry, my available time is sporadic and unpredictable today. --prime mover 17:05, 12 July 2012 (UTC)

- Hopefully, you also deem this intricacy is dealt with appropriately by my last amendment. --Lord_Farin 17:15, 12 July 2012 (UTC)

- Just the thing. --prime mover 17:54, 12 July 2012 (UTC)