In mathematics, computer science, linguistics, and philosophy a tuple is an ordered list of elements. In set theory, an <math>n</math>-tuple is a sequence of <math>n</math> elements, where <math>n</math> is a non-negative integer. There is only one 0-tuple, an empty sequence. An <math>n</math>-tuple is defined inductively using the construction of an ordered pair. Tuples are usually written by listing the elements within parentheses "<math></math>" and separated by commas; for example, <math></math> denotes a 5-tuple. Sometimes other delimiters are used, such as ...

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  1. A finite sequence of terms.
    A tuple is not merely a totally-ordered set because the same element can appear more than once in a tuple: for example, <math>(a, b, a)</math> qualifies as a 3-tuple whereas it would not qualify as a totally-ordered set (of cardinality 3), because the set would be <math>\{a, b\}</math> where <math>a \le b </math> and <math>b \le a</math> so that <math>a = b</math>; i.e., it would actually be a one-element set, <math>\{a\}</math>, not even just two-element.
    If commutativity were added to a tuple, it would turn into a multiset or "bag". For example, words (of some alphabetic language) can be considered to be tuples of letters. If the ordering requirement on those letters were lifted, then the word would become a multiset of letters equivalent to those of its anagrams.
  2. A single row in a relational database.
  3. A set of comma-separated values passed to a program or operating system as a parameter to a function call.
  4. In some programming languages, a data type which is similar but distinct from the list data type, whose instances are characterized by having a rather fixed arity, and the elements of which instances can differ from each other by data type. (Note: this definition may overlap with the previous one.)
    Both Python and Haskell have a tuple data type as well as a list data type.
    Unlike lists, tuples are not formed by consing.

The above text is a snippet from Wiktionary: tuple
and as such is available under the Creative Commons Attribution/Share-Alike License.

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