Re: infinity


Virgil wrote:
> In article <MPG.1d6a93aabe0b30e198a0b3@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > cbrown@xxxxxxxxxxxxxxxxx said:
> > > Tony Orlow (aeo6) wrote:
> > >
> > > > Exactly how many balls are inserted, that is, which is the last
> > > > ball inserted at or before noon? Can you say exactly what (it)
> > > > is?
> > >
> > > The reason that I can't answer your question isn't because I don't
> > > know, or simply can't say; it's because I don't understand what
> > > you're asking for.
> > >
> > > You seem to assume there is an obvious meaning to the phrase "the
> > > last ball"; and that therefore I should be able to name this unique
> > > thing (your use of the word "the" suggests that there would be only
> > > one).
> > >
> > > I think I could understand your meaning better if you could answer
> > > the question "when is the last time /before noon/ at which it can
> > > be said 'it is 1/(2^n) seconds before noon' for some finite natural
> > > number n?"
> > >
> > > That question is a bit simpler; it has nothing to do with vases,
> > > balls, or numbers of balls, or adding or subtracting infinities.
> > >
> > > Perhaps if you could answer that question, I could understand what
> > > you mean by "the last ball inserted".
> > >
> > > Cheers - Chas
> > >
> > >
> > If you claim the vase becomes empty, then there must be a last ball
> > removed to cause that situation.
>
> If TO claims the vase contains any naturally numbered balls, he should
> be able to name one.
>
> > You cannot identify this ball, but
> > insist on your opponents identifying a ball that remains. I ask you,
> > how many balls you have inserted, because the ball that has been in
> > the vase the longest is 1/10 of the number of that ball. Which ever
> > ball you can imagin ebing the last removed, call it n, there are nine
> > times as many NOT removed, from n+1 through 10n. So, I am asking you
> > exactly how many balls you have inserted into your vase, so I can
> > tell you which ones remain. That's only fair.
>
> Now if each ball were to have a lengthened stay in the vase, but removed
> no sooner that in the original problem, To must agree that the number of
> balls in the vase at any instant would be at least as large as before at
> that same instant.
>
> Let us change things so that the nth ball is inserted at 1+1/2^(n-1)
> minutes before noon, but stll removed at 1/2^(n-1) minutes before noon.
>
> TO must agree that each ball is now inserted before it would have been
> inserted under the original rules, ands that it is still removed at the
> same instant that it was originally removed, so that at every instant
> strictly between 1 minute to noon and noon there are more balls in the
> vase than before.
>
> But under this new scheme, the vase is obviously empty at noon.
>
> To claims a knowledge of infinite series. Let him explain this:We have
> here a case of the new series dominating the old. The new series is
> strictly greater that the old for every n in N, yet TO claims that the
> old "ends up" larger that the new.

Mathematically, the above statements are equivalent to:
infinity - 10*infinity = 0
OR
oo - 10 * oo = 0

At 1 minute before noon, number of balls added to the vase is 10 times
infinity.
Between 11:59am to noon, total number of balls removed from the vase is
infinity.
At noon, all balls are removed.

The conclusion is not totally correct because we do not know the result
of substracting an infinity from an infinity.

.

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