english: We could have omitted most of the above discussion and simply defined in this way in the first place, pointing out that for each , for all but at most countably many , and for each , for all but at most countably many .
non_english: うぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅ うぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅ