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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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 FredJeffries@gmail.com Posts: 1,845 Registered: 11/29/07
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 11, 2013 4:05 PM

On Wednesday, September 11, 2013 12:26:05 PM UTC-7, Peter Percival wrote:
> Dan Christensen wrote:
> > 0^0 = 0^0 * 0^0
> > Therefore, 0^0 = 0 or 1.

>
> > To my knowledge, there is no purely number-theoretic justification
> > for eliminating either possibility.

>
> I'm sure this
> https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zero has been
> pointed out to you (either the page or the facts on the page), so your
> claim seems to be wrong.

I notice that that page says "In most settings not involving continuity
in the exponent, interpreting 0^0 as 1 simplifies formulas and
eliminates the need for special cases in theorems"

Most settings? Are there ANY settings (not involving continuity
in the exponent) where interpreting 0^0 as 1 is inappropriate?