But that seems redundant with countable/uncountable sets, because then every countable infinite set would be even (e.g. rational numbers), and every uncountable infinite set would be odd (e.g. real numbers).
It's also not clear to me what justification there would be for a "preference" for the "even" category that way -- it seems arbitrary. Why not be odd if there exists a way to pair things off such that one is left over, and even if there isn't such a way?
It's also not clear to me what justification there would be for a "preference" for the "even" category that way -- it seems arbitrary. Why not be odd if there exists a way to pair things off such that one is left over, and even if there isn't such a way?