Re: infinity

In article <MPG.1d8a28a748fc729598a234@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> stephen@xxxxxxxxxx said:
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > > So, here is my definition of a finite quantity. All quantities x, such
> > > that 0<x
> > > <=1, are finite, and if x is finite, then 1/x is finite. Zero and all
> > > numbers
> > > within zero units of zero are infinitesimal, and their inverses are
> > > infinite.
> > > So, a finite set is one with a finite number of elements.
> >
> > > Can you work with that? I mean, it doesn't define exactly what finite
> > > means,
> > > but it does define which quantities are finite. Is there a problem with
> > > this
> > > definition?
> >
> > So according to you, there is some non-infinitesimal x such that
> > 0<x<=1 and
> >
> > 1/x = the sum of all finite k
> >
> > Please tell me what that value of x is. You do claim
> > that the sum of all finite k is finite, and so by your definition
> > it must equal 1/x for some 0<x<=1.
> >
> > Stephen
> >
> Gee, if I could tell you that infinitesimal number, then I could tell you the
> sum of all finite natural numbers, and then I could tell you the largest
> finite
> natural number, and then I could fly away on my purple Unicorn and eat
> crumpets
> with the Red Queen and play croquet with flamingoes.

TO claims the existence of things that he canneither give vaues to nor
provide existence proofs for, while denying the existence of things for
which existence proofs, or values, or both, have been provided.

For example, TO claims that the set of all finite strings is a finite
set, but cannot give any concrete upper bound or concrete proof of
existence of an upper boond for the size of that set.

We, on the other hand, have proved using standard mathematics and logic
that for every finite set of more than one finite string, there are
specific finite strings not in that set.
.

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