How ridiculous! If you called it "error message" instead of "nullity", I don't think you'd be missing anything from this theory. How can you call it a "number" when it doesn't participate in the ordering and when every operation you can do with it and any number just gives it? Hm, even right in his paper he "contrasts" nullity with the IEEE "NaN" idea and says "[nullity] means that there is no unique number on the real number line, extended by the signed infinities, that satisfies the given formula." I'm surprised that it all works out consistently. 1/infinity = 0 seems OK but then there's negative infinity too, and 1/(neginf) = 0 also, but 1/0 = infinity (not neginf). That seems scary, but I guess it works out OK in the end because all the attempts to prove infinity = neginf using these relations end up passing through nullity (aka error message)? The one that I can see is that infinity = 1/0 = 1/(-0) = -1/0 = neginf, and so you add yet another note, that a/(-b) = (-a)/b is no longer good when b is 0, in order to add in posinf and neginf as "distinct" numbers. That is, "we can define operations for any pair of numbers" but the price you pay is listing all these silly exceptions. --Joshua Zucker