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.

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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

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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 ...

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Relational database, Relational database - Relational algebra

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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 ...

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• 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

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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 ...

Including:

• Congruence relation - Modular arithmetic
• Congruence relation - Linear algebra
• Congruence relation - Universal algebra
• Congruence relation - Group theory
• Congruence relation - Ring theory
• Congruence relation - General case of kernels

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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 ...

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• Antisymmetric relation - Examples
• Antisymmetric relation - Properties containing antisymmetry

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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

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<> 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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• Canonical commutation relation - Relation to classical mechanics
• Canonical commutation relation - Representations
• Canonical commutation relation - Generalizations

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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

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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 ...

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• Bivalence and related laws - The laws
• Bivalence and related laws - Bivalence is deepest
• Bivalence and related laws - Why these distinctions might matter
• Bivalence and related laws - Future contingents
• Bivalence and related laws - Vagueness

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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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• Council on Foreign Relations - Board of Directors
• Council on Foreign Relations - Executive
• Council on Foreign Relations - Officers
• Council on Foreign Relations - Current Directors
• Council on Foreign Relations - Officers and Directors Emeriti
• Council on Foreign Relations - Other well-known members

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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 ...

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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 ...

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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

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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 x_{See 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

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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 ...

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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

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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 ...

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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

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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, < ...

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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

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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 ...

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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

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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

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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 ...

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

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