On Apr 28, 12:22 am, Salmon Egg <Salmon...@sbcglobal.net> wrote: > In article > <32c1f79d-047d-44ff-9926-fcf0e8a5d...@v2g2000vbv.googlegroups.com>, > > 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.