I think that implementing TotallyOrderable and PartiallyOrderable is a good idea. But is it useful? I mean, I don't know how much people needs really to order sets. Maybe some mathematician. But they can simply use Sage: http://doc.sagemath.org/html/en/reference/categories/sage/categories/posets.html
The real problem is NaN. If NaN would not exists, floats will be perfectly total orderable. Yes, IEEE 754-2019 defines a total order: -NaN is a number minor that -Infinity, and +NaN is a number greater than +Infinity. And a NaN is greater than another NaN if its payload is greater. But IEEE 754 says also that the division by +0 should return +Infinity, and by -0 -Infinity. On the contrary, Python decided to not adhere to IEEE 754 in this case and do a very wise choice: raise an exception. The question is: why Python does not do the same for operations that now return NaN? Raising a NanError seems to me the only way to eliminate the NaN problem. Indeed NaN was created for languages like C, that does not support exceptions. -- https://mail.python.org/mailman/listinfo/python-list
