Rich Comparisons Gotcha

[Rhamphoryncus]

On Dec 7, 4:20 pm, Steven D'Aprano <st... at REMOVE-THIS-
cybersource.com.au> 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.

Mathematically, NaNs shouldn't be comparable at all.  They should
raise an exception when compared.  In fact, they should raise an
exception when *created*.  But that's not what we want.  What we want
is a dummy value that silently plods through our calculations.  For a
dummy value it seems a lot more sense to pick an arbitrary yet
consistent sort order (I suggest just above -Inf), rather than quietly
screwing up the sort.

Regarding the mythical IEEE 754, although it's extremely rare to find
quotations, I have one on just this subject.  And it does NOT say "x
== NaN gives false".  It says it gives *unordered*.  It is C and
probably most other languages that turn that into false (as they want
a dummy value, not an error.)

http://groups.google.ca/group/sci.math.num-analysis/browse_thread/thread/ead0392e646b7cc0/a5bc354cd46f2c49?lnk=st&q=why+does+NaN+not+equal+itself%3F&rnum=3&hl=en&pli=1