Re: infinity

In article <MPG.1d62a295f82e4d0498a007@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> > >> There is no last ball.
> > >
> > > Then the vase never empties.
> >
> > If you mean that there is no last finite step after which the vase is
> > empty, you are correct. However, if all steps have been performed,
> > the vase is empty. There is no last step.
> Then it never empties, but continues getting ever more full.

The n'th ball is removed at 1/2^(n -1) minus before noon.

Which ball(s) does TO suggest remain at noon.

Consider this modification of the "game", TO.

All the balls are in the vase to start with, one for each natural
number.

At one minute to noon ball 1 is removed.
At 1/2 minute to noon, ball 2 is removed.
At 1/4 minute to noon, balll 3 is removed.
.....
At 1/2^(n-1) minutes to noon, ball n is removed.
.....


How many balls are left at noon?

The only reasonable answer is none!

But at every time before noon, there are infinitely many more balls in
the vase than in the previous problem of adding 10 and removing 1.
.

Relevant Pages

  • Re: An uncountable countable set
    ... the vase, is consistent with the fact that no balls are removed at noon? ... The only relevant question is "According to the rules set up in the ... is each ball inserted before noon also removed before noon?" ... An affirmative answer confirms that the vase is empty at noon. ...
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  • Re: An uncountable countable set
    ... Does Han claim that there is any ball put in that is not taken out? ... the vase empties". ... But in order for the vase to transition from not-empty ... If the vase ever became empty, ...
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  • Re: An uncountable countable set
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  • Re: infinity
    ... Number of balls in the vase at noon is f= OO. ... Unfortunately, if infinity gets involved, this statement alone is not sufficient to claim the vase is empty before noon. ... ball) is in the vase. ... You also keep ignoring my question. ...
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  • Re: An uncountable countable set
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