Rich Comparisons Gotcha

Steven D'Aprano steven at REMOVE.THIS.cybersource.com.au
Tue Dec 9 03:45:17 CET 2008


On Sun, 07 Dec 2008 16:24:58 -0800, George Sakkis wrote:

> On Dec 7, 6:37 pm, Steven D'Aprano <st... at REMOVE-THIS-
> cybersource.com.au> wrote:
...
>> 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.
> 
> And why doesn't this happen with the current behavior if x = y = log
> (-5) ? According to the same proof,  -5 != -5.

You're right, I was a little sloppy in my "proof". There are additional 
subtleties going on.



-- 
Steven



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