Rich Comparisons Gotcha

[Robert Kern]

Steven D'Aprano wrote:
> On Sun, 07 Dec 2008 23:20:12 +0000, Steven D'Aprano wrote:
> 
>> On Sun, 07 Dec 2008 15:32:53 -0600, Robert Kern wrote:
>>
>>> Rasmus Fogh wrote:
>>>
>>>> Current behaviour is both inconsistent and counterintuitive, as these
>>>> examples show.
>>>>
>>>>>>> x = float('NaN')
>>>>>>> x == x
>>>> False
>>> Blame IEEE for that one. Rich comparisons have nothing to do with that
>>> one.
>> There is nothing to blame them for. This is the correct behaviour. NaNs
>> should *not* compare equal to themselves, that's mathematically
>> incoherent.
> 
> Sorry, I should explain why.
> 
> Given:
> 
> x = log(-5)  # a NaN
> y = log(-2)  # the same NaN
> x == y  # Some people want this to be true for NaNs.
> 
> Then:
> 
> # Compare x and y directly.
> log(-5) == log(-2)
> # If x == y then exp(x) == exp(y) for all x, y.
> exp(log(-5)) == exp(log(-2))
> -5 == -2
> 
> 
> and now the entire foundations of mathematics collapses into a steaming 
> pile of rubble.

I didn't mean to suggest that it was incorrect, just that that particular 
surprising behavior is not related to rich comparisons. Even if the OP gets an 
__equals__() or some such, NaN will still not compare equal to NaN.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco