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Date: Sun, 13 Jul 2014 02:54:44 +1000
Subject: Re: Proposal: === and !=== operators
From: Chris Angelico <rosuav@gmail.com>
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Xref: csiph.com comp.lang.python:74385

On Sun, Jul 13, 2014 at 2:35 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> You're not going to hear me arguing that the non-reflexivity of NANs and
> SQL NULL is a bad idea, although some very smart people have:
>
> http://bertrandmeyer.com/2010/02/06/reflexivity-and-other-pillars-of-civilization/
>
> Mathematical equality is reflexive. It is fundamental to the nature of
> numbers and equality that a number is always equal to itself. To the
> degree that floats are supposed to model real numbers, they should obey
> the same laws of real numbers. However, they already fail to obey them,
> so the failure of reflexivity is just one more problem that makes
> floating point such a hard problem. Compared to floating point
> arithmetic, calculus is easy.
>

And there are plenty of other laws of real numbers that floats violate
(or, let's be generous, "approximate to rather than following
perfectly"). For instance, adding two positive (non-zero) numbers
should result in a number which is greater than either, but thanks to
rounding, that's not always true. (Not to mention that "infinity"
isn't a number, but it is a floating-point value.) The problem is not
equality comparisons, the problem is the expectation that the rules of
reals apply to floats.

ChrisA