Knowing that for a set $S$ that the $n$-fold Cartesian product is $S \times S \times S\times\cdots$ $n$ times, can $n$ be equal to zero? (Note: A Cartesian product is not the same as 'just' a set.)
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Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Sep 01 '19 at 00:32
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1Possible duplicate of What is A Set Raised to the 0 Power? (In Relation to the Definition of a Nullary Operation) – Eric Wofsey Sep 01 '19 at 01:05
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See also https://math.stackexchange.com/questions/2827670/empty-cartesian-product-what-is-mathbbr0 and https://math.stackexchange.com/questions/3205234/what-is-the-cartesian-product-of-an-empty-set-of-sets – Eric Wofsey Sep 01 '19 at 01:05
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1What do you think a Cartesian product is, if not a set? – Eric Wofsey Sep 01 '19 at 01:19
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Yes, $n$ can be zero. The cartesian product of the empty family of sets is a singleton consisting of just the empty tuple.
Geoffrey Trang
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