Definition of equivalence relation in English:

equivalence relation

noun

Mathematics Logic

A relation between elements of a set which is reflexive, symmetric, and transitive and which defines exclusive classes whose members bear the relation to each other and not to those in other classes.
〔数，逻〕等价关系
Example sentencesExamples
- We are almost ready to define an equivalence relation between hyperreal numbers.
- The ability to use this symmetrically is a part of the full equivalence relation.
- Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.
- In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups.
- You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity.

Definition of equivalence relation in US English:

equivalence relation

noun

Logic Mathematics

A relation between elements of a set that is reflexive, symmetric, and transitive. It thus defines exclusive classes whose members bear the relation to each other and not to those in other classes (e.g., “having the same value of a measured property”).
〔数，逻〕等价关系
Example sentencesExamples
- In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups.
- You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity.
- We are almost ready to define an equivalence relation between hyperreal numbers.
- The ability to use this symmetrically is a part of the full equivalence relation.
- Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.

单词	equivalence relation
释义	Definition of equivalence relation in English: equivalence relation noun Mathematics Logic A relation between elements of a set which is reflexive, symmetric, and transitive and which defines exclusive classes whose members bear the relation to each other and not to those in other classes. 〔数，逻〕等价关系 Example sentencesExamples We are almost ready to define an equivalence relation between hyperreal numbers. The ability to use this symmetrically is a part of the full equivalence relation. Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category. In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups. You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity. Definition of equivalence relation in US English: equivalence relation noun Logic Mathematics A relation between elements of a set that is reflexive, symmetric, and transitive. It thus defines exclusive classes whose members bear the relation to each other and not to those in other classes (e.g., “having the same value of a measured property”). 〔数，逻〕等价关系 Example sentencesExamples In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups. You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity. We are almost ready to define an equivalence relation between hyperreal numbers. The ability to use this symmetrically is a part of the full equivalence relation. Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.
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