[Haskell-cafe] Re: 0/0 > 1 == False

[David Roundy]

On Fri, Jan 11, 2008 at 07:10:20PM -0800, Jonathan Cast wrote:
> On 11 Jan 2008, at 10:12 AM, Achim Schneider wrote:
> 
> >David Roundy <droundy at darcs.net> wrote:
> >
> >>Prelude> let x=1e-300/1e300
> >>Prelude> x
> >>0.0
> >>Prelude> x/x
> >>NaN
> >>
> >>The "true" answer here is that x/x == 1.0 (not 0 or +Infinity), but
> >>there's no way for the computer to know this, so it's NaN.
> 
> Didn't catch this the first time around, but: only to a physicist.

I don't understand what you're saying below.  Do you mean that the
"true" answer is not 1.0, or that it's not reasonable for the computer to
call it NaN?  Since 1.0 is the answer you get for high-precision
computations, it's hard to see how you can argue that it's a wrong answer.

> (I mean no disrespect to the author of darcs, but nevertheless the  
> point stands).  Back in the real world, 0 / 0 may be defined  
> arbitrarily, or left undefined.  (Defining it breaks the wonderful  
> property that, if lim (xn) = x, lim (yn) = y, and x/y = z, then lim  
> (xn / yn) = z.  This is considered a Bad Thing by real  
> mathematicians).  In fact, in integration theory 0 * inf = 0 for  
> certain 'multiplications', which gives the lie to 0 / 0.
-- 
David Roundy
Department of Physics
Oregon State University