I need to find a partition of Z into 10 infinite sets, and for each partition, what is the corresponding equivalence relation?
so I know there's a theorem that states "let P be a partition of a nonempty set A. Then there exists an equivalence relation R on A such that P is the set of equivalence classes determined by R"
So an obvious partition of the set of integers that is infinite and is in 10 parts is the set that is 10k and another set 10k+1,...,10k+9 for an integer k.
But how can I find the corresponding relation?