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

`, and we want`

**b**`to be the "first" element of the pair, the ordered pair contains`

**a**`and`

**{a}**`. We can symbolize this`

**{a, b}**`but it is normally written`

**{{a, b}, a}**`.`

**(a, b)**
An ordered ` n`-tuple is this process carried out to use up the

`components. That is, one element (call it`

*n*`) is the first element, another (call it`

**X**_{1}`) is the second, an so on up to`

**X**_{2}`.`

**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

`becomes apparent.`

**(X**_{1},X_{2},X_{3},X_{4},X_{5})