| 单词 | equivalence relation |
| 释义 | equivalence relationequivalence relationequivalence relationEquivalence Relationequivalence relation[i′kwiv·ə·ləns ri′lā·shən]Equivalence Relationa concept in logic and mathematics expressing the presence in different objects of the same characteristics or properties. The objects are indistinguishable—identical, equal, or equivalent—with respect to such shared characteristics. Any of them can serve equally well as a “representative” of the equivalence class to which all objects between which the equivalence relation holds belong. Equivalence relations are reflexive, symmetric, and transitive. Under certain conditions and within certain limits, they possess the property of substitution—that is, objects in an equivalence class can, with certain limitations, perform the same functions and their names, or words designating them, can be substituted for each other in different propositions. Equivalence Relationan equality-type relation, that is, a binary relation that is reflexive, symmetric, and transitive. For example, if two geometric figures are congruent or similar or if two sets of objects are isomorphic or equipotent, the figures or sets are equal or identical in some regard. Thus, isomorphic sets are indistinguishable in structure if by “structure” is meant the aggregate of the properties with respect to which the sets are isomorphic. equivalence relation(mathematics)See also partial equivalence relation. |
| 随便看 |
|
英语词典包含2567994条英英释义在线翻译词条，基本涵盖了全部常用单词的英英翻译及用法，是英语学习的有利工具。