I haven't been following this thread closely, but I know enough math to say that lim_{x->0} (0/x) is 0.

When evaluating a limit, one does not simply substitute the limiting value into the expression.  The limit is the value of the expression as the variable gets arbitrarily close but not equal to the limiting value.  As x gets arbitrarily close to 0, 0/x remains exactly 0.  I have no clue, how this impacts the original issue.

Cheers.

Curtis Gehman
Burlingame, CA

On Oct 10, 2011, at 3:17 AM, Michael Powell wrote:



On Mon, Oct 10, 2011 at 3:01 AM, <Viatcheslav.Sysoltsev@h-d-gmbh.de> wrote:
On Sun, 09 Oct 2011 19:04:39 +0200, Matwey V. Kornilov <matwey.kornilov@gmail.com> wrote:

and, actually let a=b=x,

lim_{x->0} ((x-x)/min(|x|,|x|)) = lim_{x->0} (0/min(|x|,|x|)) = lim_{x->0} (0) = 0


I'am not active mathematician, but I believe lim {x->0} (0/x) is 0/0 and thus considered undefined, not 0.

I haven't run the numbers either, but 0/0 is indeed undefined or Single.NaN if you prefer.
 
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