> Also, it still has no total order This is not true. It is defined to have the exact same ordering, bitwise, as two's complement integers. That means it has t

> Also, it still has no total order This is not true. It is defined to have the exact same ordering, bitwise, as two's complement integers. That means it has total order: the NaN is the most negative, then comes the negative numbers, then zero, and then positive numbers.