Encyclopedia > Tuple

  Article Content

N-tuple

Redirected from Tuple

In mathematics, an n-tuple is a collection of objects whose order matters.

The n can be replaced by a specific number, thus one can for example say a quaternion can be represented as a 4-tuple. A 2-tuple is an ordered pair; a 3-tuple is a triple or triplet; further constructions are possible, such as octuple, but many mathematicians find it quicker to write "8-tuple", even if still pronouncing "octuple".

A general n-tuple is: (a1,a2,...,an)= (b1,b2,...,bn) iff a1=b1, a2=b2 and so on.

Formally, an n-tuple can be defined in terms of sets as either (a1,a2,...,an)= {a1,{a1,a2},{a1,a2,a3},...,{a1,a2,...an}} or as an inductive definition:

  1. a 1-tuple (a1) is just a1;
  2. if x is an n-tuple, then (x,an+1) (i.e. {x,{x,an+1}}) is an (n+1)-tuple.

It is fairly easy to show that either definition implies the property given above. However, the sets generated look very different.


Many computer programming languages support tuples as a data type, either for objects of fixed types, or as a collection of objects of any type.

The Lisp programming language originally used the ordered pair abstraction to create all of its n-tuple and list structures, similarly to the inductive definition above.


In the field of relational databases, a tuple is a row in a relation (table). An n-tuple is a row with n columns. It is important not to confuse an n-tuple with n tuples.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Ludvika

... in central Sweden, in the county of Dalarna. The municipality covers an area of 1500.7 km². Of the total population of 26450, 13112 are male, and 13338 ar ...

 
 
 
This page was created in 38 ms