Nitpick: why do you say "partially ordered" for float? If we take NaNs into account, then the float type is neither partially nor totally ordered, since x <= x is False when x is a NaN. If we don't take NaNs into account (which is probably the way we'd want to go from a practicality standpoint), it's both partially and totally ordered. (To David Mertz's earlier comment, "not a total order when you include nans and infs", infinities don't affect the existence of a total or partial order here; it's only the NaNs that we have to worry about.)

Mark