Re: infinity


William Hughes wrote:
> guenther vonKnakspot wrote:
> > William Hughes wrote:
> > > 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
> >
> > Because there is no reason for A to end up with an empty vase. A has
> > been dropping 10 balls into the vase and taking one out. The whole
> > contention that B finds the vase to be empty is that B knows that for
> > any n in the set of natural numbers, the ball labelled n is not inside
> > the vase.
> >
>
> But the whole point is that it is possible to perform the operation
> "drop 10 balls into the vase, take one out" an infinite number of
> times and end up with an empty vase. A knows this.
> So A is not surprised to see an empty vase, even though he
> does not know exactly how this happened. It is not necessary
> for A to know how he got an empty vase for A to know that the
> vase is empty.
>
> -William Hughes
Yes, and it is also possible to perform the operation "drop 10 balls
into the vase, take one out" and end up with a non empty vase. This is
the case, for example, if you take out the ball labelled 2*n, in which
you end up with a vase full of balls labelled with uneven numbers. A
would not be surprised to end up with an empty vase if performing the
experiment with unlabelled (to him/her) balls if (she/he) knew of a
proof that this is possible in advance. The proof that you can put ten
unlabelled balls into a vase take one out, repeatedly for an infinite
number of times and end up with an empty vase is eluding me. I would be
very thankful for this proof. I am not saying that any answer given up
to now is wrong, I am only trying to understand where the paradox stems
from, and wether it can be resolved.
Regards.

.

Relevant Pages

  • Re: infinity
    ... guenther vonKnakspot wrote: ... >>> balls he is putting out, and which ones he is taking out. ... >>> vase and which ones are being taken out. ... >> Why do you think that A will end up with a non empty vase? ...
    (sci.math)
  • Re: infinity
    ... >>> Why do you think that A will end up with a non empty vase? ... >>> number of balls in his vase from 0 to infinity. ... It is quite possible for a infinite set to have a proper ...
    (sci.math)
  • Re: infinity
    ... >>> Why do you think that A will end up with a non empty vase? ... >>> number of balls in his vase from 0 to infinity. ...
    (sci.math)
  • Re: infinity
    ... > guenther vonKnakspot wrote: ... Suppose the balls are not labeled on the outside but inside, ... >> vase and which ones are being taken out. ... > Why do you think that A will end up with a non empty vase? ...
    (sci.math)