ordered tuplet

The concept of ordered $n$-tuplet is the generalization of ordered pair to $n$ items. For small values of $n$, the following are used:

This notion can be defined set-theoretically in a number of ways. For convenience, we shall express two of these definitions for quintuplets — it is perfectly easy to generalize them to any other value of $n$.

One possibility is to build $n$-tuplets out of nested ordered pairs. In the case of our example $(a,b,c,d,e)$, the as a nested ordered pair looks like

$$(a,(b,(c,(d,e)))).$$

This form of is used in the programming language LISP.

Another possibility is to define $n$-tuplets as maps. In this way of thinking, a quintuplet is a function whose domain is the set $\{1,2,3,4,5\}$. In the case of our example, the function $f$ in question is defined as

Especially with the second interpretation, one sees that a synonym for ”ordered tuplet” is ”finite sequence” or ”list”. For instance, a quintuplet can also be regarded as a sequence of five items or a list of five items.