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Topic: 0^0=1
Replies: 145   Last Post: Jun 5, 2012 1:10 PM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: 0^0=1
Posted: Apr 28, 2012 8:58 AM

On Apr 28, 12:22 am, Salmon Egg <Salmon...@sbcglobal.net> wrote:
> In article
>
>  jbriggs444 <jbriggs...@gmail.com> wrote:

> > Irrelevant.
>
> > If one were trying to define 0^0 as the limit of x^y as x and y
> > jointly
> > approach zero then one might be justified in invoking L'Hopital to
> > help
> > in evaluating the limit.

>
> Point well taken but... The subject of essential singularities rather
> than indeterminate forms should be the subject.
>
> Being more of a physicist or engineer, I look for answers to problems
> rather than rigor. Look at the ridicule Heaviside got from
> mathematicians for his operational calculus used to solve real problems
> just because he was not rigorous,
>
> Most mathematicians no longer complain about operational calculus
> because Laplace transforms and other approaches have provided the
> justification for Heaviside methods.
>

Good point. I suppose that's how the bulk of basic mathematical theory
came about -- merchants, engineers and architects just improvising and
evolving in their methods. Nothing wrong with that. It was an
indispensable first step. But there comes a point when you have to dot
the i's and cross the t's -- to formalize your theory. In this case, I
don't see that much is gained by setting 0^0=1. With only a bit of
extra work -- a few more lines of proof -- you can get around this
controversy.

Dan
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