Thanks for taking the time to explain your terminology. I've found a couple of things about partial equivalence relations (one neat one was on nlab about how th

Thanks for taking the time to explain your terminology. I've found a couple of things about partial equivalence relations (one neat one was on nlab about how the construction of the reals can either be a quotient of a subset of sequences or a subset of a quotient of sequences, and partial equivalences let you reason about the latter), but everything else seems to be in textbooks about CS-specific theory. When you've talked about "partial orders" and "total orders" I'm surprised that you haven't disambiguated that you're talking about something completely different from what pretty much every mathematician would call a "partial order" or "total order." You could very well know about all this, but when you say "claiming that the correct behavior is a bug shows a dangerous lack of understanding of mathematics" but also don't mention that you're aware of the usual notion of a partial order, it seems a bit odd... > that is the one that completely breaks math. > Attempting to forcibly define it as a total relation leads only to inconsistent results. Where's the inconsistency? Or, a stronger question, why can't a NaN be the bottom of a total order (in the math sense) for floats? That is, make it be so that for all floats x, NaN <= x?