equivalence relation
[/ˌɛkwɪˈvæləns rɪˈleɪʃən/]
nounpl: equivalence relations
relação de equivalência
1. A mathematical relation that satisfies three properties: reflexivity (every element is related to itself), symmetry (if a is related to b, then b is related to a), and transitivity (if a is related to b and b is related to c, then a is related to c).
The relation of having the same remainder when divided by 5 is an equivalence relation on the set of integers.
A relação de ter o mesmo resto quando dividido por 5 é uma relação de equivalência no conjunto dos inteiros.
2. In logic and mathematics, a fundamental concept used to partition sets into equivalence classes where elements share a common property.
Congruence modulo n is a classic example of an equivalence relation.
Congruência módulo n é um exemplo clássico de uma relação de equivalência.
This is a specialized mathematical term used uniformly in both Brazilian Portuguese and Portuguese academic contexts. It is typically encountered in university-level discrete mathematics, abstract algebra, and set theory courses. The term has no colloquial usage and is restricted to formal mathematical discourse in both English and Portuguese-speaking countries.
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