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:

$\begin{matrix}n&\hbox{\sl name}\hfill&\hbox{\sl example}\hfill\\ 3&\hbox{triplet}\hfill&(a,b,c)\hfill\\ 4&\hbox{quadruplet}\hfill&(a,b,c,d)\hfill\\ 5&\hbox{quintuplet}\hfill&(a,b,c,d,e)\hfill\\ 6&\hbox{sextuplet}\hfill&(a,b,c,d,e,f)\hfill\\ 7&\hbox{septuplet}\hfill&(a,b,c,d,e,f,g)\hfill\\ 8&\hbox{octuplet}\hfill&(a,b,c,d,e,f,g,h)\hfill\\ 9&\hbox{nonuplet}\hfill&(a,b,c,d,e,f,g,h,i)\hfill\\ 10&\hbox{decuplet}\hfill&(a,b,c,d,e,f,g,h,i,j)\hfill\\ \end{matrix}$

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 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

$\begin{array}[]{ccc}f(1)&=&a\\ f(2)&=&b\\ f(3)&=&c\\ f(4)&=&d\\ f(5)&=&e\\ \end{array}$

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.

Title	ordered tuplet
Canonical name	OrderedTuplet
Date of creation	2013-03-22 14:55:44
Last modified on	2013-03-22 14:55:44
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	16
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 03-00
Synonym	tuplet
Synonym	$n$ -tuplet
Synonym	$n$ -tuplets
Synonym	ordered $n$ -tuplet
Synonym	-tuplet
Synonym	-tuplets
Synonym	tuple
Synonym	$n$ -tuple
Synonym	ordered $n$ -tupule
Synonym	-tuple
Synonym	finite sequence
Related topic	OrderedPair
Related topic	GeneralizedCartesianProduct
Defines	triplet
Defines	quadruplet
Defines	quintuplet
Defines	sextuplet
Defines	septuplet
Defines	octuplet
Defines	nonuplet
Defines	decuplet