Re: Negative zeros?

[Paul Kienzle]

On Sep 13, 2005, at 8:17 PM, Vic Norton wrote:

> I am sorry, John, David, and Stephan. I am a mathematician. I don't 
> choose to read nonsense. Zero is zero is zero.
>
> I realize that e-1000000 is positive and -e-1000000 is negative and 
> that these might be represented by 0 and -0 respectively on a machine. 
> But I will never accept that
>    0 * (-1) = -0.

So don't think of 0 as zero.  Instead think of it as an infinitesimal. 
It just happens to display as 0. Then a*0 = lim_{x->Inf} a/x = 0.  Zero 
has no floating point representation.

This is consistent with 1/0 -> Inf,  1/Inf -> 0, 1/-0 -> -Inf, 1/-Inf 
-> 0, and 0*Inf is not a number.

You also need to rationalize why -0 == 0 returns true rather than 
false.  You can do this if you think of the a==b as |a-b|<epsilon for 
all epsilon>0.  Unfortunately, this breaks down for inf==inf.  Strictly 
speaking inf==inf is not defined, especially if you use the definition 
above because inf - inf is not a number.  IEEE floating points defines 
it as true.  Rationalizations can only get you so far.

- Paul



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