1. In mathematics, two sets that have the same number of elements or the same cardinality, allowing for a one-to-one correspondence between their elements
The set of natural numbers and the set of even numbers are equivalent sets because they can be put into one-to-one correspondence.
O conjunto dos números naturais e o conjunto dos números pares são conjuntos equipotentes porque podem ser colocados em correspondência biunívoca.
2. Sets that can be matched element-for-element with no elements left over in either set
Sets A = {1, 2, 3} and B = {a, b, c} are equivalent sets.
Os conjuntos A = {1, 2, 3} e B = {a, b, c} são conjuntos equipotentes.
This is primarily a mathematical/academic term used in set theory education. It is equally formal in both English and Portuguese mathematical contexts and is not typically used in casual conversation. The term is essential in teaching abstract mathematics and is standardized across educational systems.