A
tuple is a finite ordered list of
elements. In
mathematics, an
-tuple is a
sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, an empty sequence. An -tuple is
defined inductively using the construction of an
ordered pair. Tuples are usually written by listing the elements within parentheses "
" and separated by commas; for example,
denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "[ ]" or angle brackets "< >". Braces "{ }" are never used for tuples, as they are the standard notation for
sets. Tuples are often used to describe other mathematical objects, such as
vectors. In computer science, tuples are directly implemented as
product types in most
functional programming languages. More commonly, they are implemented as
record types, where the components are labeled instead of being identified by position alone. This approach is also used in
relational algebra. Tuples are also used in relation to programming the
semantic web with
Resource Description Framework or RDF. Tuples are also used in
linguistics and
philosophy.