Concept
Tuple
Overview
In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".
Tuples are usually written by listing the elements within parentheses "( )" and separated by commas; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning.
An n-tuple can be formally defined as the image of a function that has the set of the first n natural numbers as its domain (1, 2, ..., n). Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element, for example,
(
(
(
1
,
2
)
,
3
)
,
4
)
=
(
1
,
2
,
3
,
4
)
{\displaystyle \left(\left(\left(1,2\right),3\right),4\right)=\left(1,2,3,4\right)}
.
In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples.
Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics; and in philosophy.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
All types of series are capable of formal definition, and their properties can be deduced from the principles of symbolic logic by means of the Algebra of Relatives. The notion of a limit, which is fundamental in the greater part of higher mathematics, used to be defined by means of quantity, as a term to which the terms of some series approximate as nearly as we please. But nowadays the limit is defined quite…
Bertrand Russell, Mysticism and Logic and Other Essays
States what Tuple is.
Thus there arises a classification of modes of formation, or in the language commonly used by mathematicians, a classification of Functions. Any number, considered as formed from any other number, is called a function of it; and there are as many kinds of functions as there are modes of formation. The simple functions are by no means numerous, most functions being formed by the combination of several of the…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Tuple is.
Then _R(A, B, C)_ is another eternal object of the lowest complex grade. Analogously there are eternal objects of successively higher grades. In respect to any complex eternal object, _S(D1, D2, ... Dn)_, the eternal objects _D1, ... Dn_, whose individual essences are constitutive of the individual essence of _S(D1, ... Dn)_, are called the components of _S(D1, ... Dn)_. It is obvious that the grade of complexity to…
Alfred North Whitehead, Science and the modern world
States what Tuple is.
Related ideas
- Greek language
- Philosophy
- Integer
- If and only if
- Latin
- Function (mathematics)
- Mathematics
- Mathematical object
- Model theory
- Natural number
- Number
- Ordered pair
- Linguistics
- Probability theory
- Set (mathematics)
- Set theory
- Singleton (mathematics)
- Type theory
- Domain of a function
- Combinatorics
- Computer science
- Complex number
- Cardinality
Place in the tradition
Part of First-order logic.