In article <email@example.com>, "Carl W." <firstname.lastname@example.org> wrote:
> Virgil <email@example.com> wrote in message > news://vmhjr2-A0ECCE.firstname.lastname@example.org... > > In article <IY_c7.168$Iw2.email@example.com>, > > "Duane Jones" <firstname.lastname@example.org> wrote: > > > > > "Virgil" <email@example.com> wrote in message > > > news://vmhjr2-08FC87.firstname.lastname@example.org... > > > > In article <email@example.com>, > > > > "Carl W." <firstname.lastname@example.org> wrote: > > > > > > > > > Virgil <email@example.com> wrote in message > > > > > news://vmhjr2-E3F3EE.firstname.lastname@example.org... > > > > > > > > > > > (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.