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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 ‑uple as the suffix, the original suffix was ‑ple as in "triple" (three-fold) or "decuple" (ten ...
If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). [4] One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be represented by an n-dimensional array, where each element is an n-tuple.
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 ...
Finitary relation. In mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n -tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding Xi. [1][2][3] Typically, the relation describes a possible connection between the elements of ...
Row: Tuple or record: A data set representing a single item Column: Attribute or field: A labeled element of a tuple, e.g. "Address" or "Date of birth" Table: Relation or Base relvar: A set of tuples sharing the same attributes; a set of columns and rows View or result set: Derived relvar: Any set of tuples; a data report from the RDBMS in ...
In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics. The theory was introduced by Edgar F. Codd. The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such ...
Cartesian coordinates identify points of the Euclidean plane with pairs of real numbers. In mathematics, the real coordinate space or real coordinate n-space, of dimension n, denoted Rn or , is the set of all ordered n -tuples of real numbers, that is the set of all sequences of n real numbers, also known as coordinate vectors.
According to the first meaning of permutation, each of the six rows is a different permutation of three distinct balls. In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or; the act or process of changing the linear order of an ordered set. [1]