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 **X**_{1}) is the first element, another (call it **X**_{2}) is the second, an so on up to **X**_{n}.

If you try writing out an ordered 5-tuple using the {} notation you will have 32 **X**_{i}'s and 64 curly braces, and the usefulness of the paretheses notation **(X**_{1},X_{2},X_{3},X_{4},X_{5}) becomes apparent.