The concept of ordered $n$ -tuplet is the generalization of ordered pair to $n$ items. For small values of $n$ , the following terms are used: $$\begin{matrix} n & \hbox{\sl name} \hfill & \hbox{\sl example} \hfill \\ 3 & \hbox{triplet} \hfill & (a,b,c) \hfill \\ 4 & \hbox{quadruplet} \hfill & (a,b,c,d) \hfill \\ 5 & \hbox{quintuplet} \hfill & (a,b,c,d,e) \hfill \\ 6 & \hbox{sextuplet} \hfill & (a,b,c,d,e,f) \hfill \\ 7 & \hbox{septuplet} \hfill & (a,b,c,d,e,f,g) \hfill \\ 8 & \hbox{octuplet} \hfill & (a,b,c,d,e,f,g,h) \hfill \\ 9 & \hbox{nonuplet} \hfill & (a,b,c,d,e,f,g,h,i) \hfill \\ 10 & \hbox{decuplet} \hfill & (a,b,c,d,e,f,g,h,i,j) \hfill \\ \end{matrix}$$

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 representation as a nested ordered pair looks like $$(a,(b,(c,(d,e)))).$$ This form of representation 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.