| 单词 | equivalence relation |
| 释义 | > as lemmasequivalence relation equivalence relation n. Mathematics a relation between elements of a set that is reflexive, symmetric, and transitive. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > elements in or parts of > relation between well-ordering1914 symmetric difference1936 partial ordering1938 equivalence relation1940 symmetrical difference1978 1940 E. T. Bell Devel. Math. ix. 177 A relation such as ∼ is called an ‘equivalence relation’ for the given class. 1959 E. M. Patterson Topology (ed. 2) ii. 21 Congruence and similarity in Euclidean geometry..are..equivalence relations. 1963 G. F. Simmons Introd. Topol. & Mod. Anal. i. 27 If we start with a partition, we get an equivalence relation by regarding elements as equivalent if they belong to the same partition set, and if we start with an equivalence relation, we get a partition by grouping together into subsets all elements which are equivalent to one another. 1980 A. J. Jones Game Theory iv. 194 To prove the theorem it is only necessary to verify the three defining properties of an equivalence relation... Reflexivity... Symmetry... Transitivity. < as lemmas |
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