Re: infinity

In article <1124145152.696003.73360@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"snapdragon31" <snapdragon31@xxxxxxxxx> wrote:

> Virgil wrote:

> > 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

Wrong! The "above statements" referred to make no claims at all about
arithmetic with infinite quantities.
>
> At 1 minute before noon, number of balls added to the vase is 10 times
> infinity.

Until you explain what you mean by "10 times infinity", your claim is
nonsense. Infinity is not a number to be used in arithmetic. Being
infinite and being finite are qualities that sets can have.

> Between 11:59am to noon, total number of balls removed from the vase is
> infinity.

The "number" removed is infinite, not infinity. it is a distinction that
makes a difference.

> At noon, all balls are removed.

Actually, none are removed AT noon, but all of them are removed by noon.
>
> The conclusion is not totally correct because we do not know the result
> of substracting an infinity from an infinity.

Does "snapdragon31" suggest that, under the new rules, one cannot tell
whether there are any balls left in the vase at and after noon?

Is he in any doubt that every ball inserted into the vase before noon is
also removed before noon?

If he is, he is not very bright.
.

Relevant Pages

  • Re: infinity
    ... Physically: Infinity is undefined physically. ... >> to show that each ball is removed from the vase before noon and is not ... >> the vase is empty before noon. ... The operation of adding or removal of balls is undefined at noon. ...
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  • Re: Questions about the marble problem.
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  • Re: Cantor Confusion
    ... Given the information of that Tristram Shandy story, ... vase, even though the vase is more clear about limits. ... intuition, but by logic, that the vase at any time contains more balls ... noon (finished infinity, actualized transfinity) the vase is empty is ...
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  • Re: Infinity : An interesting variant
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  • Re: An uncountable countable set
    ... number of balls in the vase at time t is 0; ... balls in the vase at noon must be infinity, ... The conclusion produces clear contradictions in terms of a time of emptying and the requirement at some point of a negative number of balls in the vase in order for it to empty at all, and it all derives from using the Zeno schedule to complete a sequence which has no end, hiding this fact in a time singularity at t=0. ...
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