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Relations

A Wisdom Archive on Relations

Relations

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relations, Relation

ARTICLES RELATED TO Relations

Relations: Encyclopedia - Relation

Relation. In mathematics, a relation is a generalization of arithmetic relations, such as "=" and "<", which occur in statements, such as "5 < 6" or "2 + 2 = 4". See relation (mathematics), binary relation (of set theory and logic) and relational algebra. In relational modeling, a relation is a set of tuples, otherwise known as a table. In logic and philosophy, a relation is a two-argument property or predicate.

Read more here: » Relation: Encyclopedia - Relation

Relations: Encyclopedia II - Relations of production - Relations of production and relations of distribution
One of the theoretical problems in Marxian economics is to distinguish exactly between relations of production and relations of distribution, determining the significance of each in the allocation of resources. According to the crudest and most vulgar interpretations of Das Kapital, exploitation occurs only at the point of production. Marx himself obviously did not assert this at all, he only postulated the command o ...

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Relations of production, Relations of production - Definitions, Relations of production - Illustration, Relations of production - Social/technical distinction and reification, Relations of production - Relations of production and relations of distribution, Relations of production - Criticism of Marx's concept

Read more here: » Relations of production: Encyclopedia II - Relations of production - Relations of production and relations of distribution

Relations: Encyclopedia II - Relational database - Relational algebra

The relational algebra is a set of operations that manipulate relations as they are defined in the relational model and as such describes part of the data manipulation aspect of this data model. Because of their algebraic properties these operations are often used in database query optimization as an intermediate representation of a query to which certain rewrite rules can be applied to obtain a more efficient version of the query. The exact set of operations may differ per definition and also depends on whether the unlabeled relation ...

See also:

Relational database, Relational database - Relational algebra

Read more here: » Relational database: Encyclopedia II - Relational database - Relational algebra

Relations: Encyclopedia - Binary relation

In mathematics, a binary relation, sometimes called dyadic relation, is a relation between two entities. It is exemplified by such ideas as "is greater than" or "is equal to" in arithmetic, "is congruent to" in geometry, and "is an element of" or "is a subset of" in set theory. Functions are also a special case of binary relations (the difference between a function and a binary relation is that a function must have a unique output for every input while relations may have any number of outputs for one input). Put in lay t ...

Including:

Read more here: » Binary relation: Encyclopedia - Binary relation

Relations: Encyclopedia - Congruence relation

In mathematics and especially in abstract algebra, a congruence relation or simply congruence is an equivalence relation that is compatible with some algebraic operation(s). Congruence relation - Modular arithmetic. The prototypical example is modular arithmetic: for n a positive natural number, two integers a and b are called congruent modulo n if a − b is divisible by n. If and , then and . This turns the equivalence (mod ...

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Read more here: » Congruence relation: Encyclopedia - Congruence relation

Relations: Encyclopedia - Antisymmetric relation

In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X, if a is related to b and b is related to a, then a = b. In mathematical notation, this is: Inequalities are antisymmetric, since for different numbers a and b not both a ≤ b and a ≥ b can be true. Note that 'antisymmetric' is not the logical negative of 'symmetric' (whereby aRb imp ...

Including:

Read more here: » Antisymmetric relation: Encyclopedia - Antisymmetric relation

Relations: Encyclopedia II - Samhan - Relations

Until the rise of Goguryeo, the external relations of Samhan were largely limited to the Chinese commanderies located in the northern part of the peninsula. The longest standing of these, the Lelang commandery, appear to have maintained separate diplomatic relations with each individual state rather than with the heads of the confederacies as such. In the beginning, the relationship was tributary: a political trading system in which "tribute" was exchanged for titles or prestige gifts. Official seals identified each tribal leader's au ...

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Samhan, Samhan - Three Hans, Samhan - Geography, Samhan - Technology, Samhan - Relations

Read more here: » Samhan: Encyclopedia II - Samhan - Relations

Relations: Encyclopedia - Canonical commutation relation

<> In physics, the canonical commutation relation is the relation among the position x and momentum p of a point particle in one dimension, where [x,p] = xp − px is the so-called commutator of x and p, i is the imaginary unit and is the reduced ...

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Read more here: » Canonical commutation relation: Encyclopedia - Canonical commutation relation

Relations: Encyclopedia - Agouti-related peptide

Agouti-related peptide (AgRP) is a neuropeptide created in the arcuate nucleus of the brain that increases appetite and decreases metabolism. It is one of the most potent and long-lasting of appetite stimulators. Understanding the role AgRP plays in weight gain may assist in developing pharmaceutical models for treating obesity. Categories: Biochemicals | Obesity Other related archivesBiochemicals, Obesity, appetite, arcuat

Read more here: » Agouti-related peptide: Encyclopedia - Agouti-related peptide

Relations: Encyclopedia - Bivalence and related laws

In logic, the laws of bivalence, excluded middle, and non-contradiction are related, but not the same. This page discusses the differences. Bivalence and related laws - The laws. For any proposition P, at a given time, in a given respect, there are three related laws: Law of bivalence: P is either true or false. Law of the excluded middle: (P or not-P) is true. Law of non-contradiction: (P and not-P) is false. Bivalence and related la ...

Including:

Read more here: » Bivalence and related laws: Encyclopedia - Bivalence and related laws

Relations: Encyclopedia - Council on Foreign Relations

The Council on Foreign Relations (CFR) is a think tank which describes itself as "dedicated to increasing America's understanding of the world and contributing ideas to U.S. foreign policy. The Council accomplishes this mainly by promoting constructive, closed debates and discussions, clarifying world issues, and publishing Foreign Affairs." It began in 1921 and is one of the most powerful private organizations with influence on U.S. foreign policy. It has about 4,000 members, including former national security officers, prof ...

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Read more here: » Council on Foreign Relations: Encyclopedia - Council on Foreign Relations

Relations: Encyclopedia - Chess-related deaths

As with most games that have a long history, chess has been associated with a number of anecdotes, and some relate to games that have resulted in the murder of one of the players involved. The reliability of many of these anecdotes is suspect, but at least some appear to be based in fact. See also. List of unusual deaths Categories: Chess history | Death ...

Read more here: » Chess-related deaths: Encyclopedia - Chess-related deaths

Relations: Encyclopedia II - Binary relation - Special types of relations

Some important classes of binary relations R over X and Y are listed below Binary relation - Total or partial. left-total: for all x in X there exists a y in Y such that xRy (this property, although sometimes also referred to as total, is different from the definition of total in the next section). right-total or surjective: for all y in Y the ...

See also:

Binary relation, Binary relation - Formal definition, Binary relation - Is a relation more than its graph?, Binary relation - Example, Binary relation - Special types of relations, Binary relation - Total or partial, Binary relation - Functional injective surjective bijective, Binary relation - Relations over a set, Binary relation - Operations on binary relations, Binary relation - Sets versus classes, Binary relation - Examples of common binary relations

Read more here: » Binary relation: Encyclopedia II - Binary relation - Special types of relations

Relations: Encyclopedia II - Equivalence relation - Generating equivalence relations

If two equivalence relations over the set X are given, then their intersection (viewed as subsets of X×X) is also an equivalence relation. This allows for a convenient way of defining equivalence relations: given any binary relation R on X, the equivalence relation generated by R is the smallest equivalence relation containing R. Concretely, the equivalence relation ~ generated by R can be described as follows: a ~ b if and only if there exist elements xSee also:

Equivalence relation, Equivalence relation - Examples of equivalence relations, Equivalence relation - Examples of relations that are not equivalences, Equivalence relation - Partitioning into equivalence classes, Equivalence relation - Generating equivalence relations, Equivalence relation - Common notions in Euclid's Elements

Read more here: » Equivalence relation: Encyclopedia II - Equivalence relation - Generating equivalence relations

Relations: Encyclopedia II - Binary relation - Operations on binary relations

If R is a binary relation over X and Y, then the following is a binary relation over Y and X: Converse: R -1, defined as R -1 = { (y, x) | (x, y) ∈ R }. A binary relation over a set is equal to its converse if and only if it is symmetric. The converse of a surjective and injective function is called its inverse. If R is a binary relation over X, then each of the following are binary relations over X ...

See also:

Binary relation, Binary relation - Formal definition, Binary relation - Is a relation more than its graph?, Binary relation - Example, Binary relation - Special types of relations, Binary relation - Total or partial, Binary relation - Functional injective surjective bijective, Binary relation - Relations over a set, Binary relation - Operations on binary relations, Binary relation - Sets versus classes, Binary relation - Examples of common binary relations

Read more here: » Binary relation: Encyclopedia II - Binary relation - Operations on binary relations

Relations: Encyclopedia II - Green's relations - The H and D relations

The remaining relations are derived from L and R. Their intersection is H: a H b if and only if a L b and a R b. This is also an equivalence relation on S. An important theorem states that the equivalence class He, where e is an idempotent, is a subgroup of S (its identity is e, and all elements have inverses), and indeed is the largest subgroup of S containing e. Fo ...

See also:

Green's relations, Green's relations - The L R and J relations, Green's relations - The H and D relations, Green's relations - Example, Green's relations - Generalisations

Read more here: » Green's relations: Encyclopedia II - Green's relations - The H and D relations

Relations: Encyclopedia II - Binary relation - Operations on binary relations

If R is a binary relation over X, then each of the following are binary relations over X: Converse: R -1 ⊆ Y × X, defined as R -1 = { (y, x) | (x, y) ∈ R }. A binary relation over a set is equal to its converse if and only if it is symmetric. The converse of a surjective and injective function is called its inverse. Reflexive closure: R =, defined as R = = {(x, < ...

See also:

Binary relation, Binary relation - Definition and examples, Binary relation - Definition, Binary relation - Remark, Binary relation - Example, Binary relation - Special types of relations, Binary relation - Relations over a set, Binary relation - Operations on binary relations, Binary relation - Examples of common binary relations

Read more here: » Binary relation: Encyclopedia II - Binary relation - Operations on binary relations

Relations: Encyclopedia II - Binary relation - Special types of relations

Some important classes of binary relations R over X and Y are: total: for all x in X there exists a y in Y such that xRy (this definition for total is different from the one in the next section). functional: for all x in X, and y and z in Y it holds that if xRy and xRz then y = z. surjective: for all y in Y there exists an x in X such that ...

See also:

Binary relation, Binary relation - Definition and examples, Binary relation - Definition, Binary relation - Remark, Binary relation - Example, Binary relation - Special types of relations, Binary relation - Relations over a set, Binary relation - Operations on binary relations, Binary relation - Examples of common binary relations

Read more here: » Binary relation: Encyclopedia II - Binary relation - Special types of relations

Relations: Encyclopedia II - Binary relation - Relations over a set

If X = Y then we simply say that the binary relation is over X. Or it is an endorelation over X. Some important classes of binary relations over a set X are: reflexive: for all x in X it holds that xRx. For example, "greater than or equal to" is a reflexive relation but "greater than" is not. irreflexive: for all x in X it holds that not xRx. "Greater than" is an example of an irreflexive relation. See also:

Binary relation, Binary relation - Formal definition, Binary relation - Is a relation more than its graph?, Binary relation - Example, Binary relation - Special types of relations, Binary relation - Total or partial, Binary relation - Functional injective surjective bijective, Binary relation - Relations over a set, Binary relation - Operations on binary relations, Binary relation - Sets versus classes, Binary relation - Examples of common binary relations

Read more here: » Binary relation: Encyclopedia II - Binary relation - Relations over a set

Relations: Encyclopedia II - Maxwell relations - Derivation of Maxwell's relations

From the theory of the thermodynamic potentials, it is known that the following relationships are true for a single phase simple fluid with a constant number of particles: If, for any potential Φ we have But we know that: which gives: which are just Maxwell's relations. For example, for the ...

See also:

Maxwell relations, Maxwell relations - Derivation of Maxwell's relations

Read more here: » Maxwell relations: Encyclopedia II - Maxwell relations - Derivation of Maxwell's relations

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Relations
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Relations
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