Re: infinity

guenther vonKnakspot wrote:
> step...@xxxxxxxxxx wrote:
> <snip>
> > > Are you saying then that one single performance of the experiment
> > > delivers one single vase which is empty for person A and simultaneously
> > > is not empty for person B, because A does not know which balls were
> > > removed while B does?
> >
> > No. How did you come to that conclusion?
> >
> > A ball is either removed or it is not. If you describe
> > exactly how the balls are removed than there is one and
> > only one answer
>
>
> Then it would appear that you did not follow my articles. Let me repeat
> for you. Suppose the balls are not labeled on the outside but inside,
> so that person A who is performing the experiment does not see which
> balls he is putting out, and which ones he is taking out. Person B has
> a device which enables him to see which balls are being put into the
> vase and which ones are being taken out. Person A performs the
> experiment every morning, untill person B determines that the
> experiment performed is exactly the one described as experiment 1 by
> the OP. Now we have a situation in which A would end up with a non
> empty vase (he has been dropping 10 indistinguishable balls into the
> vase and taking one out all morning long) while B knows that for every
> natural number n the ball labelled n has been taken out of the vase. So
> which one is it, is the vase empty or not?
>

Why do you think that A will end up with a non empty vase?
Depending on which balls A removes he may end up with any
number of balls in his vase from 0 to infinity. A does not
know what is going to happen. B waits for a day when A uses
(unintentionally since A cannot read labels) a strategy that
leads to an empty vase. Both A and B agree that the vase
is empty. (B knows the order in which A removed the balls,
A doesn't, but the fact that the balls can be labelled means
that this order exists.)

-William Hughes

.

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. ...
    (sci.math)
  • Re: An uncountable countable set
    ... To become empty means there is a change of state in the vase, from having balls to not having balls. ... There are always a specific number of balls, if additions and removals occur instantaneously. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Since the vase was empty to start with, it cannot later "become" empty after once having been empty, at least according to that definition. ... Noon does not exist in the experiment, or else you have infinitely numbered balls. ... insertion or removal or location of balls is a function of time. ...
    (sci.math)
  • Re: infinity
    ... >>> Physically or mathematical it is not difficult to prove that the vase ... # of balls in the vase can be ... this statement alone is not sufficient to claim ... >>> the vase is empty before noon. ...
    (sci.math)
  • 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. ... then the sum becomes 0. ...
    (sci.math)
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