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# Topic: Equivalence class

###### In the News (Tue 20 Aug 19)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-16) Recall that equivalence classes are distinct (their intersections are always empty) so you'll never use any of the four that we found above in any other class. Certainly two distinct elements of P(X) won't be in the same equivalence class under this new definition of the relation ~ because this can only happen when the elements are related (i.e., they are equal) and we are assuming from the outset that these two elements are distinct. Thus we have 32 distinct, one element equivalence classes. www.mathforum.org /library/drmath/view/51864.html   (698 words)

 Equivalence Class Equivalence class, a mathematical concept, is a subset of given set induced by an equivalence relation on that given set. Any two different equivalence classes are disjoint and the union over all of the equivalence classes is the given set. Equivalence classes and their corresponding equivalence relation are defined in set theory, a vital foundation for mathematics and those fields that use mathematics. www.iscid.org /encyclopedia/Equivalence_Class   (153 words)

 Equivalence Relation Equivalence relation, a mathematical concept, is a type of relation on a given set that provides a way for elements of that set to be identified with (meaning considered equivalent to for some present purpose) other elements of that set. Equivalence relation is defined in a branch of mathematics called set theory, a vital branch underpinning all branches of mathematics and those fields that use mathematics. Equivalence relations are so ubiquitous in mathematics and other fields that use mathematics because they enable the user to partition a set in a particular way of the user’s design. www.iscid.org /encyclopedia/Equivalence_Relation   (2634 words)

 Equivalence class - Wikipedia, the free encyclopedia The equivalence classes are known as right cosets of H in G; one of them is H itself. In natural language processing, an equivalence class is a set of all references to a single person, place, thing, or event, either real or conceptual. Because of the properties of an equivalence relation it holds that a is in [a] and that any two equivalence classes are either equal or disjoint. en.wikipedia.org /wiki/Equivalence_class   (764 words)

 Equivalence relations The union of all the equivalence classes is A. Thus the equivalence classes of a relation are a partition. Each equivalence relation on a set partitions the set into its equivalence classes but also for each partition of the set there is an equivalence relation whose equivalence classes are the sets in the partition. www.math.csusb.edu /notes/rel/node3.html   (490 words)

 Equivalence relation - Wikipedia, the free encyclopedia Green's relations are five equivalence relations on the elements of a semigroup. Every equivalence relation on X defines a partition of X into subsets called equivalence classes: all elements equivalent to each other are put into one class. The equivalence classes of this relation are the right cosets of H in G. en.wikipedia.org /wiki/Equivalence_relation   (869 words)

 Equivalence class - Wikipedia, the free encyclopedia In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: This operation can be thought of (very informally indeed) as the act of "dividing" the input set by the equivalence relation, hence both the name "quotient", and the notation, which are both reminiscent of division. The homotopy class of a continuous map f is the equivalence class of all maps homotopic to f. www.wikipedia.org /wiki/Equivalence_class   (764 words)

 Equivalence class -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-16) This equivalence relation is known as the (The choicest or most essential or most vital part of some idea or experience) kernel of f. Because of the properties of an equivalence relation it holds that a is in [a] and that any two equivalence classes are either equal or (Click link for more info and facts about disjoint) disjoint. It follows that the set of all equivalence classes of X forms a (A vertical structure that divides or separates (as a wall divides one room from another)) partition of X: every element of X belongs to one and only one equivalence class. www.absoluteastronomy.com /encyclopedia/e/eq/equivalence_class.htm   (956 words)

 Reference.com/Encyclopedia/Equivalence class The equivalence classes are known as right cosets of H in G; one of them is H itself. The homotopy class of a continuous map f is the equivalence class of all maps homotopic to f. Because of the properties of an equivalence relation it holds that a is in [a] and that any two equivalence classes are either equal or disjoint. www.reference.com /browse/wiki/Quotient_set   (939 words)

 Encyclopedia: Equivalence class In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i. The equivalence classes are known as right cosets of H in G. In mathematics, the kernel of a function f may be taken to be either the equivalence relation on the functions domain that roughly expresses the idea of equivalent as far as the function f can tell, or the corresponding partition of the domain. www.nationmaster.com /encyclopedia/Equivalence-class   (1727 words)

 Equivalence class   (Site not responding. Last check: 2007-10-16) In mathematics given a set X and an equivalence relation ~ on X the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a : The equivalence classes are known as cosets of H in G. The homotopy class of a continuous map f is the equivalence class of all homotopic to f. www.freeglossary.com /Equivalence_class   (1108 words)

 Up to article - Up to mathematics equivalence class group theory group action eight - What-Means.com   (Site not responding. Last check: 2007-10-16) In mathematics, the jargon term "up to xxxx" is used to describe a situation in which members of an equivalence class can be regarded as a single entity for some purpose. This means that there are two equivalence classes of groups of order 4, if we consider groups to be equivalent if they are isomorphic. In informal contexts, mathematicians often use the word modulo for the same purpose, as in "modulo isomorphism, there are two groups of order 4", or "there are 92 solutions modulo the names of the queens". www.what-means.com /encyclopedia/Up_to   (313 words)

 Equivalence Relation   (Site not responding. Last check: 2007-10-16) Equivalence relations can also be represented by a digraph since they are a binary relation on a set. The set of even numbers and that of odd numbers in the equivalence relation of congruent mod 2, and the set of integers equivalent to a number between 1 and 12 in the equivalence relation on hours in the clock example are called an equivalence class. Definition(equivalence class): For an equivalence relation R on a set A, the set of the elements of A that are related to an element, say a, of A is called the www.cs.odu.edu /~toida/nerzic/content/relation/eq_relation/eq_relation.html   (649 words)

 Unsolved: Equivalence Relations Run through all the equivalence classes one by one, probably by means of their canonical elements. One clear application for equivalence classes with a disconnect operation is the algorithm that constructs a deterministic finite state machine from a nondeterministic one (used in regular expression processing). Most of the character set can be treated as equivalent: any character not mentioned explicitly in the regular expression behaves just the same as any other, and any two characters that are always used as part of the same character class are equivalent. www.chiark.greenend.org.uk /~sgtatham/algorithms/equivalence.html   (427 words)

 Equivalence class establishment, expansion, and modification in preschool children.   (Site not responding. Last check: 2007-10-16) Equivalence class establishment, expansion, and modification in preschool children. Equivalence classes were established with more participants in the latter group, replicating prior research with participants with retardation. Four participants, in whom equivalence classes were established and who were available for further participation, were exposed to new conditional discriminations without trial-by-trial feedback and involving some novel and some familiar stimuli. seab.envmed.rochester.edu /abstracts/JeabAbstracts/71/_71-195.Htm   (204 words)

 Section (ii) A Novice's Inquiry on the Concept of Equivalence Class and of Coset: Bestowing Meaning Through Ambivalent ... Underlying her questions seems to be her difficulty with the new notions of equivalence class and, most severely, with the notion of coset. G), the tutor prefers to represent an element a of the domain as a dot and its equivalence class (generally defined as the set of elements in the domain that are mapped on the same value as a) as a line segment. It seems that commonly used phrasing such as 'define a correspondence between the elements of a group and their equivalence classes' is not perceived by the novice as a clear establishment of a function; or in C3 Camille does not see the = sign as a sign of definition but as a sign of equality. www.uea.ac.uk /~m011/thesis/chapter9/9ii.htm   (1364 words)

 Class and equivalence [Jan 2002; 95-3] Class effect is usually taken to mean similar therapeutic effects and similar adverse effects, both in nature and extent. Equivalence trials should have a prior definition of how big a difference is a difference, and justify it. Designating a class effect on a group of drugs, and judging them to be equivalent on inadequate evidence is something most of us do at some time or another. www.jr2.ox.ac.uk /bandolier/band95/b95-3.html   (1424 words)

 Imam Transfer of Response Speed They reported the formation of two five-member equivalence classes for two participants whose accuracy performances were inverse functions of nodality on post-transfer tests. The post-transfer nodality effect suggests, of course, that the equivalence class members were not equally related to one another with respect to the new response function. Such evidence of nonsubstitutability of equivalence class members is problematic because by virtue of their class membership they should be substitutable for one another, ipso facto, due to their common history of reinforcement (Fields et al., 1995; Sidman, 1990, 1994; Sidman, Wynne, Maguire, & Barnes, 1989; cf. www.eahb.org /Imam/ImamTransfer.htm   (2421 words)

 Psychological Record, The: Effects of training directionality and class size on equivalence class formation by adults   (Site not responding. Last check: 2007-10-16) Equivalence classes are more likely to emerge after comparison-as-node (CaN) instead of sample-as-node (SaN) training for pigeons, typically developing children, and individuals with mental retardation, but not for typically functioning older children or adults. Four parameters that define the structure of any equivalence class are (a) number of stimuli in the class, (b) number of nodal stimuli in a class, (c) distribution of singles among the nodal stimuli, and (d) directionality of training (Fields, Adams, & Verhave, 1993; Fields & Verhave, 1987). Magnitude of equivalence was indexed by degree of response suppression. www.findarticles.com /p/articles/mi_qa3645/is_199910/ai_n8863585   (1308 words)

 Lecture #5 Equivalence classes may be identified from a functional description by carefully examining the constraints and functional requirements for each input. That is, valid equivalence classes for input values that are valid (may be determined from the constraints) and invalid equivalence classes for input values that are invalid (may be determined from the constraints). You would identify one valid equivalence class for input values where the first character is a letter and one invalid equivalence class where the first character is not a letter. condor.depaul.edu /~jmorgan1/se433.lect5.html   (3917 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-16) Recall that equivalence classes are distinct (their intersections are always empty) so you'll never use any of the four that we found above in any other class. Certainly two distinct elements of P(X) won't be in the same equivalence class under this new definition of the relation ~ because this can only happen when the elements are related (i.e., they are equal) and we are assuming from the outset that these two elements are distinct. After you've compute the class associated with a particular element, just pick an element that doesn't belong to any of the classes that have already been determined. mathforum.org /library/drmath/view/51864.html   (727 words)

 Psychological Record, The: Untrained temporal differentiation and equivalence class formation   (Site not responding. Last check: 2007-10-16) Once such stimulus classes are developed, subjects are able to match members within each class to other members within the class even though they have had no direct training on those matches. Of those reports of the transfer of discriminative functions, two studies in particular have focused on the transfer of control that is of a temporal nature; that is, derived control by stimuli in the presence of which temporal properties of responding appear to be differentiated. Stimuli that enter into equivalence relations, however, have been related only indirectly during training, and thus the transfer of stimulus functions through equivalence relations may be considered a more unequivocal demonstration of derived stimulus control. www.findarticles.com /p/articles/mi_qa3645/is_199807/ai_n8803915   (1105 words)

 Semple Analysis Engine: semple::analysis::LocationEquality class Reference   (Site not responding. Last check: 2007-10-16) The equivalence classes can be constructed directly from nothing or generated from the static field relation graph based on equivalences in the abstract program state. Integer location equivalence classes are primary used by the loop analysis to perform inductive proofs of location equivalence. For every pair of locations (x, y) x and y are in the same equivalence class iff there is a path of equality relation edges from x to y and the initial values at x and y are equivalent. www.cs.rpi.edu /~gregod/Semple/classsemple_1_1analysis_1_1LocationEquality.html   (234 words)

 EQUIVALENCE CLASS An equivalence class is a subset whose elements are related to each other by an equivalence relation. The equivalence classes of a set under some relation form a partition of that set (i.e. Specialty definitions using "EQUIVALENCE CLASS": equivalence class partitioning, equivalence relation ♦ projective plane. www.websters-online-dictionary.org /definition/english/EQ/EQUIVALENCE+CLASS.html   (210 words)

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