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In mathematics, a tuple is a finite ordered list (sequence) of elements. An n-tuple is a sequence (or ordered list) of n elements, where n is a non-negative integer. There is only one 0-tuple, an empty sequence, or empty tuple, as it is referred to. An n-tuple is defined inductively using the construction of an ordered pair. In mathematics, a tuple is a finite ordered list (sequence) of elements. An n-tuple is a sequence (or ordered list) of n elements, where n is a non-negative integer. There is only one 0-tuple, an empty sequence, or empty tuple, as it is referred to. An n-tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write 'tuples' by listing the elements within parentheses ' ( ) {displaystyle ({ ext{ }})} ' and separated by commas; for example, ( 2 , 7 , 4 , 1 , 7 ) {displaystyle (2,7,4,1,7)} denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets '' or angle brackets '⟨ ⟩'. Braces '{ }' are only used in defining arrays in some programming languages such as C++ and Java, but not in mathematical expressions, as they are the standard notation for sets. The term tuple can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. In dynamically typed languages, such as Lisp, lists are commonly used as tuples. 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. The term originated as an abstraction of the sequence: single, double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n‑tuple, ..., where the prefixes are taken from the Latin names of the numerals. The unique 0‑tuple is called the null tuple. A 1‑tuple is called a singleton, a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple or triplet. The number n can be any nonnegative integer. For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as an 8‑tuple, and a sedenion can be represented as a 16‑tuple. Although these uses treat ‑tuple as the suffix, the original suffix was ‑ple as in 'triple' (three-fold) or 'decuple' (ten‑fold). This originates from medieval Latin plus (meaning 'more') related to Greek ‑πλοῦς, which replaced the classical and late antique ‑plex (meaning 'folded'), as in 'duplex'. The general rule for the identity of two n-tuples is Thus a tuple has properties that distinguish it from a set.

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