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Topic: Leaving 0^0 undefined -- A number-theoretic rationale
Replies: 48   Last Post: Sep 15, 2013 1:06 PM

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 Robin Chapman Posts: 412 Registered: 5/29/08
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 13, 2013 2:50 AM

On 13/09/2013 06:41, Dan Christensen wrote:
> Playing around with a calculator, I found the following:

You needed a calculator!

> If x=0 and y is a very small positive real number, then we have
> x^y=0. Shifting x just slightly into the positive suddenly results in
> x^y being very close to 1.
>
> Nothing earth-shattering here, but it seems to reinforce my
> recommendation that 0^0 ought to be left undefined for any real-world
> applications. f(x,y)=x^y simply behaves too strangely close to the
> origin.

In other words x^y cannot be extended to a continuous function at (0,0).

So, why if your interests concern integers, does the behaviour of
real a real variable function influence you so much?