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Topic: Antisymmetric relation

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	Binary relation - Wikipedia, the free encyclopedia
		In mathematics, the concept of binary relation, sometimes called dyadic 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.
		Put in lay terms, a binary relation is a statement about two objects that may be true or false depending on the choice of objects, for example, "4 is less than 5" is true, and the relation is "is less than".
		A binary relation that is functional is called a partial function; a binary relation that is both total and functional is called a function.
	en.wikipedia.org /wiki/Hierarchical_relationship (1260 words)

	Antisymmetric relation - Wikipedia, the free encyclopedia
		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.
		There are relations which are both symmetric and antisymmetric (equality), relations which are neither symmetric nor antisymmetric (divisibility on the integers), relations which are symmetric and not antisymmetric (congruence modulo n), and relations which are not symmetric but are anti-symmetric ("is less than").
		The relation "is less than or equal to" is not symmetric but is antisymmetric, and the antisymmetric condition is not vacuous.
	en.wikipedia.org /wiki/Antisymmetric_relation (219 words)

	Antisymmetric relation
		In mathematics, a binary relation R over a set X is antisymmetric if it holds for all a and b in X that if aRb and bRa then a = b.
		The relation < on the integers is also anti-symmetric; since a < b and b < a is impossible, the antisymmetry condition is vacuously true.
		There are relations which are both symmetric and anti-symmetric (equality), there are relations which are neither symmetric nor anti-symmetric (divisibility on the integers), there are relations which are symmetric and not anti-symmetric (congruence modulo n), and there are relations which are not symmetric but anti-symmetric (less-than on the integers).
	www.ebroadcast.com.au /lookup/encyclopedia/an/Antisymmetric.html (151 words)

	Equality (mathematics) article - Equality (mathematics) equality mathematics binary predicate equivalence relation ... (Site not responding. Last check: 2007-10-22)
		Equivalence in the general sense is provided by the construction of a equivalence relation between two elements.
		Given a set A, the restriction of equality to the set A is a binary relation, which is at once reflexive, symmetric, antisymmetric, and transitive.
		The binary relation "is approximately equal" between real numbers or other things, even if more precisely defined, is not transitive (it may seem so at first sight, but many small differences can add up to something big).
	www.what-means.com /encyclopedia/Equals (767 words)

	Reflexive relation article - Reflexive relation mathematics binary relation equality subset inequality divisibility - ... (Site not responding. Last check: 2007-10-22)
		In mathematics, a binary relation R over a set X is reflexive if for all a in X, a is related to itself.
		A reflexive relation that is also transitive is a preorder.
		A preorder that is symmetric, is an equivalence relation.
	www.what-means.com /encyclopedia/Reflexive (123 words)

	Antisymmetric - Wikipedia, the free encyclopedia
		In set theory, the adjective antisymmetric usually refers to an antisymmetric relation.
		The term "antisymmetric function" is sometimes used for odd function, although some meanings of antisymmetric are essentiality f(y,x) = -f (x,y).
		In linear algebra and theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (usually the exchange of two indices, which becomes the transposition of the matrix) is performed.
	en.wikipedia.org /wiki/Antisymmetric (157 words)

	lec11Sept
		A relation is antisymmetric if there is never an edge from both a to b and b to a, when a and b are different.
		A relation is asymmetric if there is never an edge from both a to b and from b to a, and there are no loops.
		A relation is transitive if whenever there is an edge from a to b and from b to c, there is an edge completing the triangle by going from a to c directly.
	www.pitt.edu /~vanlehn/cs0441/lec21Oct.html (861 words)

	Antisymetric - It should be recognized that trajectory control in these magnets could be implemented via a fast ...
		A relation R defined on a set S is antisymetric iff; whenever x R y and y R on the set of integers is antisymetric.
		Antisymmetric antisymmetric A relation on A is antisymmetric iff,.
		Antisymmetric Relation -- from MathWorld Antisymmetric Relation -- from MathWorld A relation R on a set S is antisymmetric provided that distinct elements are never both related to one another.
	www.destarter.com /antisymmetric/antisymetric.html (526 words)

	Read about Antisymmetric relation at WorldVillage Encyclopedia. Research Antisymmetric relation and learn about ... (Site not responding. Last check: 2007-10-22)
		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.
		There are relations which are both symmetric and antisymmetric (equality), relations which are neither symmetric nor antisymmetric (divisibility on the
		An antisymmetric relation that is also transitive and reflexive is a
	encyclopedia.worldvillage.com /s/b/Antisymmetric_relation (226 words)

	PowerLoom Manual: Built-In Relations
		A frame predicate is a second-order relation that is used to describe constraints on the set of fillers for a binary relation applied to an instance.
		Relation that specifies a lower bound on the cardinality of the set of fillers of the relation ?r applied to ?i.
		Relation that specifies an upper bound on the cardinality of the set of fillers of the relation ?r applied to ?i.
	www.isi.edu /isd/LOOM/PowerLoom/documentation/manual/manual_10.html (2785 words)

	Partially ordered set - Wikipedia, the free encyclopedia
		Such an ordering does not necessarily need to be total, that is, it need not guarantee the mutual comparability of all objects in the set.
		A partial order is a binary relation R over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b and c in P, we have that:
		In these contexts a strict (or irreflexive) partial order is a binary relation which is irreflexive and transitive, and therefore asymmetric.
	www.wikipedia.org /wiki/Partial_order (449 words)

	lec11Sept
		A relation from set A to set B is a set of ordered pairs (x,y) such that xÎA and yÎB.
		A symmetric relation on A: "xÎA "yÎA [ (x,y)ÎR -> (y,x)ÎR ]
		An asymmetric relation on A: "xÎA "yÎA [ (x,y)ÎR -> (y,x)ÏR.]
	www.pitt.edu /~vanlehn/cs0441/lec16Oct.html (254 words)

	Antisymmetric - Wikipedia
		A binary relation R over a set X is antisymmetric if it holds for all a and b in X that if aRb and bRa then a = b.
		Note that antisymmetry is not the opposite of symmetry (aRb implies bRa), that is, it does not necessarily hold for an antisymmetric relation that aRb implies that not bRa.
		In fact, a binary relation can be antisymmetric and symmetric at the same time if, and only if, no two different elements are related.
	nostalgia.wikipedia.org /wiki/Antisymmetric (139 words)

	The Ultimate Symmetric relation - American History Information Guide and Reference (Site not responding. Last check: 2007-10-22)
		In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.
		There are relations which are both symmetric and antisymmetric (equality), there are relations which are neither symmetric nor antisymmetric (divisibility), there are relations which are symmetric and not antisymmetric (congruence modulo n), and there are relations which are not symmetric but are anti-symmetric ("is less than or equal to").
		A symmetric relation that is also transitive and reflexive is an equivalence relation.
	www.historymania.com /american_history/Symmetric_relation (148 words)

	Order Relation
		Example 4: The relation {< 1, 1 >, < 1, 2 >, < 1, 3 >, < 2, 3>, < 3, 3 > } on the set of integers {1, 2, 3} is neither reflexive nor irreflexive.
		Thus in an antisymmetric relation no pair of elements are related to each other.
		(b) is neither reflexive nor irreflexive, and it is antisymmetric, symmetric and transitive.
	www.cs.odu.edu /~toida/nerzic/content/relation/property/property.html (550 words)

	Binary relation (Site not responding. Last check: 2007-10-22)
		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.
		It may also be thought of as a binary function that takes as arguments an element x of X and an element y of Y and evaluates to true or false (indicating whether the ordered pair (x, y) is an element of the set which is the relation).
		If a binary relation is also a binary function injective and onto, the converse is called inverse of the function.
	www.sciencedaily.com /encyclopedia/binary_relation (941 words)

	Antisymmetric relation (Site not responding. Last check: 2007-10-22)
		The relation < on the integers is also anti-symmetric; since a < b and b < a isimpossible, the antisymmetry condition is vacuously true.
		There are relations which are both symmetric andanti-symmetric (equality), there are relations which are neither symmetric nor anti-symmetric (divisibility on the integers), there are relations which aresymmetric and not anti-symmetric (congruence modulo n), and there are relations which are not symmetric but anti-symmetric(less-than on the integers).
		The relation less-than-or-equal (<=) on the integers is not symmetric but isanti-symmetric, and the anti-symmetric condition is not vacuous.
	www.therfcc.org /antisymmetric-relation-232012.html (177 words)

	PlanetMath: antisymmetric
		Antisymmetric is not the same thing as ``not symmetric'', as it is possible to have both at the same time.
		This is version 10 of antisymmetric, born on 2002-02-02, modified 2005-02-28.
		Object id is 1666, canonical name is Antisymmetric.
	planetmath.org /encyclopedia/Antisymmetry.html (69 words)

	Read about Binary relation at WorldVillage Encyclopedia. Research Binary relation and learn about Binary relation here! (Site not responding. Last check: 2007-10-22)
		mathematics, the concept of binary relation is exemplified by such ideas as "is greater than" and "is equal to" in
		functions are a special case of binary relations.
		A relation which is reflexive, antisymmetric and transitive is called a
	encyclopedia.worldvillage.com /s/b/Binary_relation (1051 words)

	antisymmetric (Site not responding. Last check: 2007-10-22)
		Definition: A binary relation R for which a R b and b R a implies a = b.
		The relation "is married to" is symmetric, but not antisymmetric: if Paul is married to Marlena, then Marlena is married to Paul (symmetric), but Paul and Marlena are not the same person.
		Equals (=) is antisymmetric because a = b and b = a implies a = b.
	www.nist.gov /dads/HTML/antisymmetric.html (157 words)

	The algebra of sets - Wikipedia, the free encyclopedia
		In the case of arithmetic, it is elementary algebra that develops the fundamental properties of arithmetic operations and relations.
		For example, the operations of addition and multiplication obey familiar laws such as associativity, commutativity and distributivity, while, the "less than or equal" relation satisfies such laws as reflexivity, antisymmetry and transitivity.
		It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion.
	www.umsl.edu /~siegel/SetTheoryandTopology/The_algebra_of_sets.html (1016 words)

	PlanetMath: anti-symmetric
		is anti-symmetric, then the polarization of the anti-symmetry relation gives the condition:
		Cross-references: determinant, group, generate, transpositions, cycle notation, proposition, parity, permutation, multi-linear, equivalent, characteristic, relation, polarization, mapping, bilinear, field, vector spaces
		Object id is 2826, canonical name is AntiSymmetric.
	planetmath.org /encyclopedia/Antisymmetric.html (150 words)

	Equivalence Relation
		When a relation is derived from a set crossed with itself, several important properties become meaningful.
		A relation possessing all three properties is called an equivalence relation.
		The relation r is a partial ordering on the set s, or s is a partially ordered set via r, or s is a poset, if r is transitive and antisymmetric.
	www.mathreference.com /set,rst.html (1016 words)

	Rock, Paper, Scissors - Wikipedia, the free encyclopedia
		A transitive relation R is one for which a R b and b R c implies a R c.
		A reflexive, antisymmetric, and transitive relation on a set is known as a partial ordering, from which notions of "greater" and "less" follow.
		A game option which is "greater" than another is closer to being optimal, but such a notion does not exist in Roshambo: The relation used to determine which throws defeat which is non-transitive.
	en.wikipedia.org /wiki/Rock_paper_scissors (2553 words)

	Surreal number - Wikipedia, the free encyclopedia
		If we want the generated numbers to represent numbers then the ordering that is defined upon them should be a total order.
		However, the relation ≤ defines only a total preorder, i.e., it is not antisymmetric.
		Since this defines an equivalence relation the ordering on the equivalence classes implied by ≤ will be a total order.
	www.wikipedia.com /wiki/Surreal+numbers (3289 words)

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