Congruence
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As an abstract term, congruence means similarity between objects. Congruence, as opposed to equivalence or approximation, is a relation which implies a kind of equivalence, though not complete equivalence.
In mathematics, congruence is formally represented by a triple-tilde [(\cong)], whereas approximation is represented by the double-tilde [(\approx)]. In both cases, the single tilde (~) may sometimes be used as a substitute (which may cause confusion due to its usage in logic and computer programming languages for representing negation). Congruence modulo n is usually denoted "≡" (see congruence relation for an example).
- In arithmetic and algebra, congruence refers to a congruence relation.
- In euclidean geometry, congruence refers to the equivalence of shapes. See congruence (geometry).
- In the theory of smooth manifolds, especially in the context of general relativity, Congruence (general relativity) refers to the integral curves defined by a vector field.
- In psychology and NLP, congruence could be defined as rapport within oneself, or internal and external consistency, perceived by others as sincerity or certainty.
- In cladistics, congruence is a test of homology, or shared, derived character states, in which the distributions of supposed homologies among taxa are compared for consistency.
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