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Topic: 0! = 1
Replies: 25   Last Post: Oct 8, 2003 6:35 AM

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Virgil

Posts: 1,119
Registered: 12/6/04
Re: 0! = 1
Posted: Aug 14, 2001 3:31 PM
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In article <3b78f3d7.0@katana.legend.co.uk>,
"Carl W." <no-one@dev.null> wrote:

> Virgil <vmhjr2@home.com> wrote in message
> news://vmhjr2-A0ECCE.21141910082001@news1.denver1.co.home.com...

> > In article <IY_c7.168$Iw2.8744@petpeeve.ziplink.net>,
> > "Duane Jones" <gauss@ziplink.net> wrote:
> >

> > > "Virgil" <vmhjr2@home.com> wrote in message
> > > news://vmhjr2-08FC87.16133710082001@news1.denver1.co.home.com...

> > > > In article <3b73c07e.0@katana.legend.co.uk>,
> > > > "Carl W." <no-one@dev.null> wrote:
> > > >

> > > > > Virgil <vmhjr2@home.com> wrote in message
> > > > > news://vmhjr2-E3F3EE.23043509082001@news1.denver1.co.home.com...
> > > > >

> > > > > > (2) if n! = n*(n-1)!, and n = 1, what is (n-1)!?
> > > > >
> > > > > This is a slightly dodgy argument in that we could say the same for

> n =
> > > 0.
> > > > >
> > > > > i.e. if n! = n((n-1)!), and n = 0, what is (n-1)!?

> > > >
> > > >
> > > > Not so. Anyone can solve 1 = 1*x for x, which defines x = 0! but how
> > > > do you solve 1 = 0*x for x, which is needed to define x = (0-1)! ?

> > >
> > >
> > > How so? In (2) above, 1! can only be defined after knowing 0!. You
> > > inadvertently assume 1! = 1 to show that 0! = 1.
> > >
> > > Cheers,
> > > Duane
> > >
> > >
> > >

> >
> > You are not following the thread. Carl W. assumed 1! = 1 but that 0!
> > was naturally undefined.
> >
> > Carl W. then said that if 0! could be found from 1! by downward use
> > of the relation n! = n*(n-1)!, then (0-1)! be found from 0!
> > similarly.
> >
> > I was refuting that thesis.

>
> Yikes!
>
> I return to the newsgroup to realise I seem to have opened a can of worms,
> and a nasty one at that... :(
>
> Virgil - You seem to be under the misapprehension that I claim that (0-1)!
> can be found from 0!, when in fact we are arguing the same corner. I was
> saying that the definition given in the post I replied to was slightly dodgy
> because it *allowed* for the bad definition of (0-1)! as 1/0, which in most
> definitions of number, isn't valid. Controversially, we _could_ say that
> that was a valid definition in some 'definite infinity' extensions of the
> integers/reals, but normally this is not the case.
>
> The intention in my post was to define factorial solely on integers, which
> is what I presume it was originally defined as when the function was first
> used.
>
> Mario G. is obviously correct in saying that 'factorial' may be extended
> onto the reals (or further) by using the Gamma function, but my intention
> was for a 'purer' factorial - the schoolboy integers-only definition if you
> will.
>
> Many apologies for creating a proto-flamewar, :(
> Carl
>
>


I think you meant to say tha t you were defining n! for _positive_
integers n, rather than _all_ integers, since under no circumstances
is there a standard definition of n! for negative integers n.







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