[Steven D'Aprano]
.... 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
py> NAN < 23 or NAN > 23

(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 :-)