equivalence class
[/ɪˈkwɪvələns klæs/]
nounpl: equivalence classes
classe de equivalência
1. A subset of a set formed by grouping elements that are related by an equivalence relation, where all elements in the class are equivalent to each other and to no elements outside the class
In the set of integers, the equivalence class of 5 modulo 3 contains all integers that leave remainder 5 when divided by 3.
No conjunto dos inteiros, a classe de equivalência de 5 módulo 3 contém todos os inteiros que deixam resto 5 quando divididos por 3.
2. A mathematical partition of a set where each element belongs to exactly one class based on satisfying reflexive, symmetric, and transitive properties
The equivalence classes partition the entire set into disjoint subsets.
As classes de equivalência particionam o conjunto inteiro em subconjuntos disjuntos.
This is a specialized mathematical term used primarily in academic and technical contexts in both Brazil and the United States. It is fundamental to abstract algebra, set theory, and discrete mathematics courses taught in universities. There is no colloquial usage outside of mathematical discourse.
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