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Relation Of Degree Zero
A relation of degree zero, 0-ary relation, or nullary relation is a relation with zero attributes. There are exactly two relations of degree zero. One has cardinality zero; that is, contains no tuples at all. The other has cardinality 1 contains the unique 0-tuple.:56 The zero-degree relations represent true and false in relational algebra.:57 Under the closed-world assumption, an ''n''-ary relation is interpreted as the extension of some ''n''-adic predicate: all and only those ''n''-tuples whose values, substituted for corresponding free variables in the predicate, yield propositions that hold true, appear in the relation. A zero-degree relation is therefore interpreted as the extension of the 0-adic predicate . The zero-degree relation with cardinality zero therefore represents false because it contains no tuples that yield a true proposition, and the zero-degree relation with cardinality 1 represents true because it contains the unique 0-tuple that yields a true propos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nullary
Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In logic and philosophy, it is also called adicity and degree. In linguistics, it is usually named valency. Examples The term "arity" is rarely employed in everyday usage. For example, rather than saying "the arity of the addition operation is 2" or "addition is an operation of arity 2" one usually says "addition is a binary operation". In general, the naming of functions or operators with a given arity follows a convention similar to the one used for ''n''-based numeral systems such as binary and hexadecimal. One combines a Latin prefix with the -ary ending; for example: * A nullary function takes no arguments. ** Example: f()=2 * A unary function takes one argument. ** Example: f(x)=2x * A binary function takes two arguments. ** Example: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Operator
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation ''on a set'' is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a ''binary operation''. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may be called simply binary functions. Binary operations are the keystone of most algebraic structures that are studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Element
In mathematics, an identity element, or neutral element, of a binary operation operating on a set is an element of the set that leaves unchanged every element of the set when the operation is applied. This concept is used in algebraic structures such as groups and rings. The term ''identity element'' is often shortened to ''identity'' (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with. Definitions Let be a set equipped with a binary operation ∗. Then an element of is called a if for all in , and a if for all in . If is both a left identity and a right identity, then it is called a , or simply an . An identity with respect to addition is called an (often denoted as 0) and an identity with respect to multiplication is called a (often denoted as 1). These need not be ordinary additi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty Set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure zero (which is not necessarily empty). The empty set may also be called the void set. Notation Common notations for the empty set include "", "\emptyset", and "∅". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabets. In the past, "0" was occasionally used as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tweedledum And Tweedledee
Tweedledum and Tweedledee are characters in an English nursery rhyme and in Lewis Carroll's 1871 book ''Through the Looking-Glass, and What Alice Found There''. Their names may have originally come from an epigram written by poet John Byrom. The nursery rhyme has a Roud Folk Song Index number of 19800. The names have since become synonymous in western popular culture slang for any two people whose appearances and actions are identical. Lyrics Common versions of the nursery rhyme include: :Tweedledum and Tweedledee : Agreed to have a battle; :For Tweedledum said Tweedledee : Had spoiled his nice new rattle. :Just then flew down a monstrous crow, : As black as a tar-barrel; :Which frightened both the heroes so, : They quite forgot their quarrel.I. Opie and P. Opie, ''The Oxford Dictionary of Nursery Rhymes'' (Oxford University Press, 1951, 2nd edn., 1997), p. 418. Origins The words "Tweedl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugh Darwen
Hugh Darwen is a computer scientist who was an employee of IBM United Kingdom from 1967. to 2004, and has been involved in the development of the relational model. Work From 1978 to 1982 he was a chief architect on Business System 12, a database management system that faithfully embraced the principles of the relational model.. He worked closely with Christopher J. Date and represented IBM at the ISO SQL committees (JTC1 SC32 WG3 Database languages,. WG4 SQL/MM.) until his retirement from IBM. Darwen is the author of The Askew Wall and co-author of The Third Manifesto, a proposal for serving object-oriented programs with purely relational databases without compromising either side and getting the best of both worlds, arguably even better than with so-called object-oriented databases. From 2004 to 2013 he lectured on relational databases at the Department of Computer Science, University of Warwick (UK), and from 1989 to 2014 was a tutor and consultant for the Open Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (relational Algebra)
In relational algebra, a projection is a unary operation written as \Pi_( R ), where R is a relation and a_1,...,a_n are attribute names. Its result is defined as the set obtained when the components of the tuples in R are restricted to the set \ – it ''discards'' (or ''excludes'') the other attributes. In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation onto attribute list (age) yields – we have discarded the names, and only know what ages are present. Projections may also modify attribute values. For example, if R has attributes a, b, c, where the values of b are numbers, then \Pi_( R ) is like R, but with all b-values halved.http://www.csee.umbc.edu/~pmundur/courses/CMSC661-02/rel-alg.pdf ''See Problem 3.8.B on page 3'' Related concepts The closely related concept in set theory (see: projection (set theory)) differs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Algebra
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. 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 databases, chief among which is SQL. Relational databases store tabular data represented as relations. Queries over relational databases often likewise return tabular data represented as relations. The main purpose of the relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express potentially complex queries that transform potentially many input relations (whose data are stored in the database) into a single output relation (the query results). Unary operators ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Join
In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. 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 databases, chief among which is SQL. Relational databases store tabular data represented as relations. Queries over relational databases often likewise return tabular data represented as relations. The main purpose of the relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express potentially complex queries that transform potentially many input relations (whose data are stored in the database) into a single output relation (the query results). Unary operators ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation (database)
In database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d1, d2, ..., dn), where each element dj is a member of Dj, 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 relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a type or data type). An attribute value is an attribute name paired with an element of that attribute's domain, and a tuple is a ''set'' of attribute values in which no two distinct elements have the same name. Thus, in some accounts, a tuple is described as a function, mapping names to values. A set of attributes in which no two distinct elements have the same name is called a heading. It follows from the above definitions that to every tuple there corresponds a unique heading, being the set of names from the tup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Element
In mathematics, an identity element, or neutral element, of a binary operation operating on a set is an element of the set that leaves unchanged every element of the set when the operation is applied. This concept is used in algebraic structures such as groups and rings. The term ''identity element'' is often shortened to ''identity'' (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with. Definitions Let be a set equipped with a binary operation ∗. Then an element of is called a if for all in , and a if for all in . If is both a left identity and a right identity, then it is called a , or simply an . An identity with respect to addition is called an (often denoted as 0) and an identity with respect to multiplication is called a (often denoted as 1). These need not be ordinary additi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
