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Re: 0^0=1
Posted:
May 4, 2012 11:54 PM
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On May 4, 7:52 pm, Marshall <marshall.spi...@gmail.com> wrote:
> On Friday, May 4, 2012 10:48:57 AM UTC-7, Dan Christensen wrote:
> > On May 4, 12:01 pm, Gus Gassmann <horand.gassm...@googlemail.com>
> > wrote:
>
> > > or is it not, since it
> > > represents a product over an empty list? Or are some products over
> > > empty lists cool, while others aren't? And who is going to keep score
> > > of which is which? DC?
>
> > Call me old-fashioned, but I will continue to avoid the use of the
> > notion "empty products." I haven't yet been convinced that it is all
> > that necessary.
>
> That doesn't make you old fashioned; it just means that
> you're not at as high a level of understanding with these
> concepts as some people are.
>
I see.
> > > Fact is, sums, products, minima, maxima and string concatenations can
> > > be defined consistently over empty lists, and one should do so in
> > > order to avoid unnecessary case distinctions.
>
> > > Of course I do understand that this has nothing to do with 0^0, which
> > > clearly is undefined in a more fundamental way. The most _useful_
> > > convention, however, is to define 0^0 = 1.
>
> > Useful or convenient though it may be, I will continue to do it the
> > hard way, case by case. I hope that doesn't sound patronizing.
>
> Again, it's not patronizing, it's just a reflection of how good
> you are with abstraction. In general, case analysis is a fine
> tool, but it's not as good a tool as more general abstractions
> give you.
>
Sorry, this is just too much like theology for my liking, Marshall. I
need a reason to believe beyond mere convenience.
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Also see video demo
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