ordered tuplet

The conceptMathworldPlanetmath of ordered n-tuplet is the generalizationPlanetmathPlanetmath of ordered pairMathworldPlanetmath 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 β€” 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


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 interpretationMathworldPlanetmathPlanetmath, 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