in reply to More Fun with Zero!
According to this math link, there's
still some discussion over what the result should be.
Update: it starts with
According to some Calculus textbooks, 0^0 is an "indeterminate form." What mathematicians mean
by "indeterminate form" is that in some cases we think about it as having one value, and in other
cases we think about it as having another. which is
slightly different than what ariels says. I guess
I think 1994 is recent, but the real discussion took place
in the 19th century...
However, read the link, don't let us read it for you.
Re: Re: More Fun with Zero! by ariels (Curate) on Jul 23, 2001 at 13:10 UTC 
 [reply] 

However there is a valid question over what we should
get back from a computer when we calculate
0^{0}. If we are thinking in terms of doing an
exact calculation, then there is no question, there is
an answer we should give and that answer is 1. But if
we are thinking in terms of floating point math, then
what the computer should be designed in terms of is,
I have a number close to 0 raised to the power of
another number close to 0 and I need to give back
something that I know is close to the answer.
In that case the computer should give up because the real
answer might be anywhere between 0 and 1 inclusive.
Therefore of his examples, all of the answers make sense.
The two products which are designed to be working with
floating point extensively (ie Excel and his calculators)
think in terms of roundoff error and decide that they
cannot give a reasonable answer. The remaining products
are all programming tools, dealing with integers, and
are assuming for one reason or another that they are dealing
with an exact integer calculation. So all of them give back
the answer 1.
(OK, I admit it, probably the calculators and Excel were
designed by people who remembered that 0^{0} was
an indeterminate form but have no idea what that really
means. But there are calculational contexts in which
failing to give an answer in that case makes sense.)
 [reply] 

I would think it's the other way around. Floatingpoint numbers are not exact, and there is a little fuzzyness to them because there is a finite number of bits. So, a value x in a register is really x±δ. If you compute f(x) and the function exists and is wellbehaved for all points in the interval xδ...x+δ, but happens to be undefined only at exactly x, then perhaps the caller really meant some other value in that range of uncertainty, and could not represent it exactly in the register. It makes sence to use the limit, when the limit is welldefined and the same for positive and negative directions.
For division by zero, division by a very very small number that got rounded to zero, if you did keep the actual number, would be an overflow anyway. The limit here is infinity. The negative and positive directions are not equal. It can't guess whether your number was actually a tad above zero or a tad under zero, and even if it did would get an overflow anyway, so it really can't help.
—John
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