A special kind of set, built from n objects, where n is an integer greater than zero. An ordered N-tuple has the same structure as the finite ordinal with N elements, but not necessarily the same elements.

An ordered 1-tuple is the set containing its single constituent, that is, {a} silly, ain't it?.

An ordered pair is an ordered 2-tuple. If we call its two constituents a and b, and we want a to be the "first" element of the pair, the ordered pair contains {a} and {a, b}. We can symbolize this {{a, b}, a} but it is normally written (a, b).

An ordered n-tuple is this process carried out to use up the n components. That is, one element (call it X1) is the first element, another (call it X2) is the second, an so on up to Xn.

If you try writing out an ordered 5-tuple using the {} notation you will have 32 Xi's and 64 curly braces, and the usefulness of the paretheses notation (X1,X2,X3,X4,X5) becomes apparent.

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