Re: infinity

stephen@xxxxxxxxxx said:
> imaginatorium@xxxxxxxxxxxxx wrote:
>
> > stephen@xxxxxxxxxx wrote:
> >> *** T. Winter <***.Winter@xxxxxx> wrote:
> >> > In article <MPG.1d8247bfb0e3e29d98a1cb@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >> > ...
> >> > > That was a proof? All it is is a rehashed statement that there is no largest
> >> > > finite integer. Sure, finite F can always be incremented, since finite k can
> >> > > always be incremented. That lack of a largest element, or longest string,
> >> > > doesn't prove infinitude of the set, as far as I'm concerned, so that doesn't
> >> > > prove anything to me.
> >>
> >> > How *do* you define finite and infinite?
> >>
> >> However he defines finite, if he claims that
> >> F = sum S^k for all finite k
> >> is finite, then he claims that
> >> F = S^F + (sum S^k for all finite k<>F)
> >> and it follows that
> >> F > S^F
>
> > Not necessarily. Try replacing "finite" with "not imponderably
> > enormous".
> > I think this last line just means that some numbers on the threshold of
> > imponderability are larger than some other such numbers, even though
> > those are also threshold values. You see, imponderability is a bit hard
> > to tie down, and frankly the arguments you mathematicians habitually
> > use don't work too well on it.
>
> I do not think that matters. Suppose that
> F = sum S^k for all not imponderably enormous k
> and that F is not imponderably enormous.
>
> Then
> F = F + (sum S^k for all not imponderably enormous k <> F)
>
> Presumably if F is not imponderably enormous than we can
> safely substract it from both sides. So
> 0 = (sum S^k for all not imponderably enormous k <> F)
>
> Well 1,2,3, etc are all not imponderably enormous, and
> S^1 + S^2 + S^3 > 0
> for S>0.
>
> Tony is basically claiming that "finite" numbers exist
> that are greater than the sum of all "finite" numbers,
> including themselves. This is going to be problematic
> for whatever definition of "finite" you plug in.
>
> Stephen
>
I am claiming no such thing. You are the one supposing a largest finite in your
stuff above, hence the contradiction. I never claimed to have any number for
the sum of all finite numbers.
--
Smiles,

Tony
.

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