.... I'd just like to point out that given the existence of float NANs, there's a case to be made for having separate <> and != operators with != keeping the "not equal" meaning and the <> operator meaning literally "less than, or greater than".
py> NAN != 23 True py> NAN < 23 or NAN > 23 False
(I'm not making the case for this, just pointing out that it exists...)
There would be precedent too: at least one of Apple's SANE maths libraries back in the 1990s had a full set of NAN-aware comparison operators including IIRC separate "not equal" and "less than or greater than" comparisons.
But I think this is a corner of IEEE-754 esoterica that probably doesn't need to be a builtin operator :-)
The 754 standard's section 5.7 (Comparisons) defines 26(!) distinct
comparison predicates. I bet SANE supplied all of them - and quite possibly nothing else in the world ever bothered (the standard _required_ only a relative few of them).
I never had the slightest interest in garbaging-up Python with syntax for all those, so never even mentioned it in the early days.
My secret plan ;-) was that if someone agitated for it enough to sway Guido, I'd add a
math.ieee_compare(x, y, raise=False)
function that returned one of the four bit constants IEEE_(LESS, EQUAL, GREATER, UNORDERED} (with values 1, 2, 4, 8), and raised some spelling of "invalid operation" iff `raise` was True and at least one of the comparands was a NaN. That's enough to build any of the standard's predicates (and a few more essentially useless ones, like "always true").
Then, e.g., for your <> above
def "<>"(x, y): return ieee_compare(x, y) & (IEEE_LESS | IEEE_GREATER) != 0
and != above would add IEEE_UNORDERED to the bits checked in that.
Then it's equal easy to build oddballs like "unordered or greater" and "only equal but raise an exception if a NaN is compared" too.
I've been quite relieved that, after all these years, nobody else seemed to care about this either :-)