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Re: Re: Re: 0^0 = 1?

On Jan 25, 2009, at 7:48 PM, Murray Eisenberg wrote:

> The arguments being exchanged about this are essentially pointless,
> except to elucidate what those various starting points are and what  
> each
> implies about 0^0.  None of them leads to a definitive conclusion  
> about
> this or that being the value of 0^0.


To this let us add the distinction between the word "undefined",  
which means that we assign no meaning to the term or collection of  
symbols, and the word (often misspelled "indeterminant")  
"indeterminate".  The latter is properly used only in the context of  
a limit, but is often used loosely of collections of symbols like  
"0^0".  When we say "0^0 is indeterminate", we really mean that Limit 
[u[x]^v[x], x -> a], where both Limit[u[x], x -> a] = 0 and Limit[v 
[x], x -> a] = 0, cannot be evaluated without further analysis of u,  
v, and the relationship between them.

--Lou Talman
   Department of Mathematical and Computer Sciences
   Metropolitan State College of Denver


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