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Equivalence relationships exist between exact copies of the same manifestation of a work or between an original item and reproductions of it, so long as the intellectual content and authorship are preserved. Examples include reproductions such as copies, issues, facsimiles and reprints, photocopies, and microfilms.
Equivalence relations are a ready source of examples or counterexamples. For example, an equivalence relation with exactly two infinite equivalence classes is an easy example of a theory which is ω-categorical, but not categorical for any larger cardinal number.
Cross-cultural research entails a particular statistical problem, known as Phylogenetic autocorrelation: tests of functional relationships (for example, a test of the hypothesis that societies with pronounced male dominance are more warlike) can be confounded because the samples of cultures are not independent. Traits can be associated not only ...
Measurement invariance or measurement equivalence is a statistical property of measurement that indicates that the same construct is being measured across some specified groups. [1] For example, measurement invariance can be used to study whether a given measure is interpreted in a conceptually similar manner by respondents representing ...
An example is the relation "is equal to", because if a = b is true then b = a is also true. If R T represents the converse of R, then R is symmetric if and only if R = R T. [2] Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. [1]
Fig.1: Wineglass model for IMRaD structure. The above scheme shows how to line up the information in IMRaD writing. It has two characteristics: the first is its top-bottom symmetric shape; the second is its change of width, meaning the top is wide, and it narrows towards the middle, and then widens again as it goes down toward the bottom.
Five references are provided early on: two textbooks, a specialized monograph on aldol reactions, and two review articles. Most readers would assume that the bulk of the statements in the comparatively short Wikipedia article could be verified by checking any of these references, and so it may only be necessary to provide additional in-line references for controversial statements, for recent ...
For example, "being isomorphic" is an equivalence relation on groups, and the equivalence classes, called isomorphism classes, are not sets. The set of all equivalence classes in X {\displaystyle X} with respect to an equivalence relation R {\displaystyle R} is denoted as X / R , {\displaystyle X/R,} and is called X {\displaystyle X} modulo R ...