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Topic: 0^0=1
Replies: 145   Last Post: May 7, 2012 8:08 AM

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 Marshall Posts: 1,928 Registered: 8/9/06
Re: 0^0=1
Posted: May 5, 2012 1:35 PM

On Friday, May 4, 2012 8:43:55 PM UTC-7, Dan Christensen wrote:
> On May 4, 7:48 pm, Marshall <marshall.spi...@gmail.com> wrote:
> > On Friday, May 4, 2012 9:01:55 AM UTC-7, Gus Gassmann wrote:
> >

> > > 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.

> >
> > Yes; more generally, the n-ary form of any binary function with
> > an identity can (should!) be defined to be that identity in the
> > arity-0 case. For example:
> >
> > AND(true, false, true) = false;
> > AND(true, false) = false;
> > AND(true) = true;
> > AND() = true;
> >
> > All the same reasoning for empty products applies. This is
> > widely understood in the CS field.
> >
> > (Min and max have identities for quantities like 32-bit integer
> > but don't in the general case.)
> >
> > Gus's earlier example program was entirely canonical and
> > ordinary; Dan's suggestion to complicate it by adding
> > extra checking make for a worse program.
> >

>
> Under what conditions should a product function return a value of 1?
> How about only when the the numbers supplied to it multiply to give
> you 1.

Yes, exactly. Just like Gus's code does, and the LISP n-ary product
does, and the earlier mentioned fold function present in functional
languages.

Marshall

Date Subject Author
5/1/12 Jesse F. Hughes
5/1/12 David W. Cantrell
5/1/12 Dan Christensen
5/1/12 Dan Christensen
5/2/12 David W. Cantrell
5/2/12 Dan Christensen
5/2/12 Frederick Williams
5/2/12 Dan Christensen
5/2/12 Frederick Williams
5/2/12 Dan Christensen
5/2/12 Frederick Williams
5/2/12 Dan Christensen
5/2/12 Frederick Williams
5/2/12 Dan Christensen
5/2/12 Michael Stemper
5/2/12 Dan Christensen
5/2/12 Jussi Piitulainen
5/2/12 Frederick Williams
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5/2/12 Rotwang
5/2/12 Dan Christensen
5/2/12 jbriggs444@gmail.com
5/2/12 Dan Christensen
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5/2/12 William Hale
5/3/12 Dan Christensen
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