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Topic: Binary relation


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In the News (Tue 23 Jul 19)

  
  NationMaster - Encyclopedia: Binary relation
Binary relations are used in many branches of mathematics to model concepts like "is greater than", "is equal to", and "divides" in arithmetic, "is congruent to" in geometry, "is adjacent to" in graph theory, and many more.
A binary relation that is functional is called a partial function; a binary relation that is both left-total and functional is called a function.
In mathematics, the concept of binary relation is exemplified by such ideas as "is greater than" and "is equal to" in arithmetic, or "is congruent to" in geometry, or "is an element of" or "is a subset of" in set theory.
www.nationmaster.com /encyclopedia/Binary_relation   (3803 words)

  
 Kids.Net.Au - Encyclopedia > Binary relation   (Site not responding. Last check: 2007-10-14)
A binary relation is a mathematical concept to do with "relations", such as "is greater than" and "is equal to" in arithmetic, or "is an element of" in set theory.
Formally, a binary relation over a set X and a set Y is a ordered triple R=(X, Y, G(R)) where G(R), called the graph of the relation R, is a subset of X × Y.
Relations over a set If X = Y then we simply say that the binary relation is over X.
www.kids.net.au /encyclopedia-wiki/bi/Binary_relation   (555 words)

  
 Binary Relation
With the definition of a relation explicitly stated, one is able to not only construct examples, but also define an algebra (used vaguely, not as the mathematical concept in the branch of mathematics called algebra) on relations.
In symbols, for a relation R from X to Y and S from Y to X, RS is not, in general, equal to SR.
Another interesting topic in the study of relation is the study of relation on a set X. In this case, both the domain and range of the relation are subsets of X. On these relations, mathematicians use a few adjectives to describe the different elementary types of relation on a given set.
www.iscid.org /encyclopedia/Binary_Relation   (2105 words)

  
 NationMaster - Encyclopedia: Partially ordered set
In other words, for all a, b, and c in P, we have that: In mathematics, the concept of binary relation is exemplified by such ideas as is greater than and is equal to in arithmetic, or is congruent to in geometry, or is an element of or is a subset of in set theory.
In mathematics, a directed set is a set A together with a binary relation and#8804; having the following properties: a and#8804; a for all a in A (reflexivity) if a and#8804; b and b and#8804; c, then a and#8804; c (transitivity) for any two a and b in A, there...
A partial order is a binary relation R over a set P which is reflexive, antisymmetric and transitive.
www.nationmaster.com /encyclopedia/Partially_ordered_set   (1992 words)

  
 Binary relation
A binary relation over a set is equal to its converse if and only if it is symmetric.
Similarly, the "subset of" relation needs to be restricted to have domain and codomain P(A) (the power set of a specific set A): the resulting set relation can be denoted.
Also, the "member of" relation needs to be restricted to have domain A and codomain P(A) to obtain a binary relation which is a set.
www.brainyencyclopedia.com /encyclopedia/b/bi/binary_relation.html   (1940 words)

  
 Binary relation
Formally, a binary relation over a set X and a set Y is an ordered triple R=(X, Y, G(R)) where G(R), called the graph of the relation R, is a subset of the Cartesian product X × Y.
It is common practice to identify the relation with its graph, i.e.
If a binary relation is also a binary function injective and onto, the converse is called inverse of the function.
www.xasa.com /wiki/en/wikipedia/b/bi/binary_relation.html   (929 words)

  
 Relations : Software Foundations : Thomas Alspaugh : UCI
is a relation that is reflexive, symmetric, and transitive.
) is a relation that is antisymmetric and transitive.
It is true, however, that the union of a relation with its converse is a symmetric relation.
www.ics.uci.edu /~alspaugh/foundations/relation.html   (1159 words)

  
 BINARY RELATION - GoGoSearch.com
Binary relations are also heavily used in computer science, especially within the relational model for databases.A binary relation is a special case of a k-ary relation">k-ary relation, that is, a set of k-tuples where the j
The sets X and Y are called the domain and codomain, respectively, of the relation, and G is called its graph.The statement (x,y) ∈ G is read "x is R''-related to y", and is denoted by xRy or R(x,y).
According to this view, the set of pairs {(1,2),(1,3),(2,7)} is a relation from any set that contains {1,2} to any set that contains {2,3,7}.Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition, inverse relation, and so on.
www.gogosearch.com /wiki/binary_relation   (1710 words)

  
 Relation (mathematics) - Wikipedia, the free encyclopedia
Relations that involve two places or roles are called binary relations by some and dyadic relations by others, the latter being historically prior but also useful when necessary to avoid confusion with binary (base 2) numerals.
From the more abstract viewpoints of formal logic and model theory, the relation L is seen as constituting a logical model or a relational structure that serves as one of many possible interpretations of a corresponding k-place predicate symbol, as that term is used in predicate calculus.
Another variation reserves the term 'relation' to the corresponding logical entity, either the logical comprehension, which is the totality of intensions or abstract properties that all of the elements of the relation in extension have in common, or else the symbols that are taken to denote these elements and intensions.
en.wikipedia.org /wiki/Relation_(mathematics)   (1774 words)

  
 Total order help – Wiki at Help.com   (Site not responding. Last check: 2007-10-14)
In mathematics, a total order, linear order, simple order, or (weak) ordering on a set X is any binary relation on X that is antisymmetric, transitive, and total.
Thus a total order is also a partial order, that is, a binary relation which is reflexive, antisymmetric and transitive.
This relation is transitive (a < b and b < c implies a < c) and, unlike ≤, trichotomous (i.e., exactly one of a < b, b < a and a = b is true).
www.help.com /wiki/Total_order   (458 words)

  
 No Title   (Site not responding. Last check: 2007-10-14)
Binary relations are particularly useful because they have two kinds of compact visual representation, tables and graphs.
The parent of relations, ``x is a parent of y'', is a binary relation between pairs of people.
This relation is reflexive, symmetric, and transitive, and hence is an equivalence relation.
www.cs.sunysb.edu /~cse113/ref/lecture22/lecture22.html   (978 words)

  
 Notation
Binary relation: A binary relation R in V is such that for any two elements
The concept of binary relation itself is too general for practical use.
Transitive relation: A relation R is transitive when aRb and bRc imply aRc, i.e.
www.unesco.org /webworld/idams/advguide/Chapt2_2_2.htm   (386 words)

  
 Definition of Relation   (Site not responding. Last check: 2007-10-14)
A relation in everyday life shows an association of objects of a set with objects of other sets (or the same set) such as John owns a red Mustang, Jim has a green Miata etc. The essence of relation is these associations.
However, {<1, 1>, <1, 4>, <3, 5>} is not a binary relation from A to B because 1 is not in B.
The parent-child relation is a binary relation on the set of people.
www.cs.odu.edu /~toida/nerzic/content/relation/definition/definition.html   (470 words)

  
 Binary relation - Term Explanation on IndexSuche.Com
is a mathematical concept to do with "relations", such as "is greater than" and "is equal to" in arithmetic, or "is an element of" in set_theory.
A relation which is reflexive, symmetric and transitive is called an equivalence_relation.
A relation which is reflexive, antisymmetric and transitive is called a partial_order.
www.indexsuche.com /Binary_relation.html   (828 words)

  
 Relations and Functions
For example, the relation `taller than,' given that we're talking about humans, can be defined as the set of all pairs of humans (x, y) such that x is taller than y.
As another example, consider the relation `greater than,' where the domain in question is the set of natural numbers {0, 1, 2, 3, 4, }.
A binary relation on two sets A and B is a subset of A x B.
www.rpi.edu /~faheyj2/SB/LCU/lcu.driver/node12.html   (485 words)

  
 PlanetMath: relation
An example of a binary relation is the less-than relation on the integers, i.e.,
This is version 8 of relation, born on 2001-10-06, modified 2006-12-04.
Object id is 122, canonical name is Relation.
planetmath.org /encyclopedia/TernaryRelation.html   (131 words)

  
 Binary relation
Formally, a binary relation over a set X and a set Y is an ordered triple R=(X, Y, G(R)) where G(R), called the graph of the relation R, is a subset of X × Y.
Some important properties that binary relations over a set X may or may not have are: ; reflexive: for all x in X it holds that xRx.
A relation which is trichotomous is called a total order or a linear order.
www.fact-index.com /b/bi/binary_relation.html   (509 words)

  
 G-Systems
The diminished seventh chord is a class of M(2,12) with 3 transpositions.
Binary system G(2,k) is a special case of G-system, n=2.
In a binary system (base E(A) ={0, 1}) it is easy to express structure of instances.
www.sweb.cz /vladimir_ladma/english/music/articles/dide99.htm   (1781 words)

  
 About at Binary Bonsai
The ‘Binary Bonsai’ is a weblog run by the earthling Michael Heilemann since March 15th, 2003.
And also because of that, Binary Bonsai has been 2nd most linked blog on Technorati, though this was after it was removed from the official list (on which it peaked at 8th place due to Kubrick’s link influence.
Binary Bonsai is run on a Media Temple server, out of Los Angeles, and has been powered by WordPress since ya days of old, as well as a veritable slew of plugins.
www.binarybonsai.com /about   (982 words)

  
 PlanetMath: operations on relations
Some operations on binary relations yield unary relations.
Cross-references: disjoint union, function, base points, unary relations, operation, symmetry, reflexivity, transitive, anti-symmetric, symmetric, Reflexive, identity element, relation ons, property, obvious, integers, terms, power, associativity, complement, inverse, composition, unary, binary relation, product, subset, relation
This is version 6 of operations on relations, born on 2006-12-04, modified 2007-03-06.
www.planetmath.org /encyclopedia/RelationComposition.html   (238 words)

  
 BINARY   (Site not responding. Last check: 2007-10-14)
A binary relation states how two kinds of elements are linked, e.g., "is married to", "is talking with", "is larger than", "precedes".
A binary alphabet contains two kinds of characters, e.g., "0" and "1", "yes" and "no." A distinction, e.g.
between "inside" and "outside", is a binary operation.
pespmc1.vub.ac.be /ASC/BINARY.html   (59 words)

  
 IEC - IEC in action | SI zone > Prefixes for binary multiples
The answers are all in IEC 60027-2, developed by TC 25 (Quantities and units, and their letter symbols), published in November 2000 and now gradually being adopted in the IT world.
A ‘bit’ is a binary digit and a ‘byte’ is a group of bits, usually eight (hence, incidentally, the French ‘octet’ for a byte).
The new prefixes and symbols for binary multiples standardized in IEC 60027-2 are not part of the SI metric system of units.
www.iec.ch /zone/si/si_bytes.htm   (1023 words)

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