[Python-Dev] Why is nan != nan?

[Alexander Belopolsky]

On Wed, Mar 24, 2010 at 3:26 PM, Mark Dickinson <dickinsm at gmail.com> wrote:
..
> Here's an interesting recent blog post on this subject, from the
> creator of Eiffel:
>
> http://bertrandmeyer.com/2010/02/06/reflexivity-and-other-pillars-of-civilization/

It appears that Meyer's view has evolved over the years:

"""
In this context it doesn't particularly shock me that operations on
NaN should cause invariant violations. After all, isn't NaN supposed
to mean "not a number"? If it's not a number, it doesn't have to
satisfy the properties of numbers.
"""
"NaN and floating point exceptions" by Roger Browne quoting an  ISE
Eiffel mailing list post by Bertrand Meyer

http://teameiffel.blogspot.com/2006/04/nan-and-floating-point-exceptions.html

Compare this with the conclusion he reached in "Pillars:"

"It is rather dangerous indeed to depart from the fundamental laws of
mathematics. "


To bring the discussion back on topic for python-dev, I would argue
that reflexivity should hold for hashable values.  Having it otherwise
would lead to unsurmountable problems when storing such values in sets
or using them as keys in dictionaries.  If x == x is False stays for x
= float('nan'), I would argue that hash(float('nan')) should raise
NotImplemented or ValueError.