The term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n‑tuple, ..., … 展开

The general rule for the identity of two n-tuples is
$${\displaystyle (a_{1},a_{2},\ldots ,a_{n})=(b_{1},b_{2},\ldots ,b_{n})}$$ if and only if 展开

In discrete mathematics, especially combinatorics and finite probability theory, n-tuples arise in the context of various counting problems and are … 展开

• Arity
• Coordinate vector
• Exponential object
• Formal language
• Multidimensional Expressions (OLAP) 展开

There are several definitions of tuples that give them the properties described in the previous section.
Tuples as functions
The $${\displaystyle 0}$$-tuple may be identified as the empty function. For $${\displaystyle n\geq 1,}$$ 展开

In type theory, commonly used in programming languages, a tuple has a product type; this fixes not only the length, but also the underlying types of each component. Formally:
and the 展开

• D'Angelo, John P.; West, Douglas B. (2000), Mathematical Thinking/Problem-Solving and Proofs (2nd ed.), Prentice-Hall, ISBN 978-0-13-014412-6
• Keith Devlin, … 展开