Definition: Suppose T is an index set and for each t in T, X_t is a non-void set. Then the(adsbygoogle = window.adsbygoogle || []).push({}); product[itex]\Pi_{t \in T}X_t[/itex] is the collection of all "sequences" [itex]\{x_t\}_{t \in T} = \{x_t\}[/itex] where [itex]x_t \in X_t[/itex].

Does this mean that [itex]\Pi_{t\inT}X_t[/itex] is the set containing all possible sequences defined by: "i-th element is a member of the set X_i"?

And by the way, if sequences are sets of ordered elements, why aren't they noted using parentheses instead of braces? Afterall, isn't an n-tuple (x_1,...,x_n) just a set whose elements are ordered, i.e. a sequence?

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# Do I have this definition right? (and a suprise bonus question on sequences!)

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