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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".
That is, the Cartesian product of a set of n-tuples with a set of m-tuples yields a set of "flattened" (n + m)-tuples (whereas basic set theory would have prescribed a set of 2-tuples, each containing an n-tuple and an m-tuple). More formally, R × S is defined as follows:
Another basic notion is the set of atomic values that contains values such as numbers and strings. Our first definition concerns the notion of tuple, which formalizes the notion of row or record in a table: Tuple A tuple is a partial function from attribute names to atomic values. Header A header is a finite set of attribute names. Projection
Product type (also called a tuple), a record in which the fields are not named; String, a sequence of characters representing text; Union, a datum which may be one of a set of types; Tagged union (also called a variant, discriminated union or sum type), a union with a tag specifying which type the data is
In relational algebra, a projection is a unary operation written as ,..., (), where is a relation and ,..., are attribute names. Its result is defined as the set obtained when the components of the tuples in R {\displaystyle R} are restricted to the set { a 1 , . . . , a n } {\displaystyle \{a_{1},...,a_{n}\}} – it discards (or excludes ) the ...
New tuples can supply explicit values or be derived from a query. Similarly, queries identify tuples for updating or deleting. Tuples by definition are unique. If the tuple contains a candidate or primary key then obviously it is unique; however, a primary key need not be defined for a row or record to be a tuple. The definition of a tuple ...
Although tuples are created by separating items with commas, the whole construct is usually wrapped in parentheses to increase readability. An empty tuple is denoted by (), while a tuple with a single value can be created with (1,). Sets (class set) are mutable containers of hashable items [15] of arbitrary types, with no duplicates. The items ...
The basic relational building block is the domain (somewhat similar, but not equal to, a data type). A tuple is a finite sequence of attributes, which are ordered pairs of domains and values. A relation is a set of (compatible) tuples. Although these relational concepts are mathematically defined, those definitions map loosely to traditional ...