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**Jhevon** by the way, here's the problem that i am having here. we only need one representative from each equivalent class. so i figure 0 could stand in for the integers, since the integers would be one equivalence class. however, i am not sure what would be the representatives for the rationals and irrationals. surely we can't have just one for each set. but there are probably infinitely many equivalence classes for each. i suppose i'd have to describe the set in words, but i can't find the words