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Tuple. In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. 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 ...
Relational algebra is a branch of mathematics that studies the manipulation and analysis of data in relational databases. It defines a set of operations, such as selection, projection, join, and union, that can be applied to relations or sets of tuples. Learn more about the concepts and notation of relational algebra on Wikipedia, including the rename operation that changes the attribute name ...
Tuple relational calculus. Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far ...
Relation (database) In database theory, a relation, as originally defined by E. F. Codd, [ 1] is a set of tuples (d 1 ,d 2 ,...,d n ), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a ...
As a bijection from a set to itself, a permutation is a function that performs a rearrangement of a set, termed an active permutation or substitution. An older viewpoint sees a permutation as an ordered arrangement or list of all the elements of S, called a passive permutation. [17]
The relational model ( RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, [ 1][ 2] where all data is represented in terms of tuples, grouped into relations. A database organized in terms of the relational model is a ...
e. Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
For example, if we write (,) for n-tuples of real numbers, then : (,) would be the type of a function which, given a natural number n, returns a tuple of real numbers of size n. The usual function space arises as a special case when the range type does not actually depend on the input.