Re: infinity


Tony Orlow (aeo6) wrote:
> Jesse F. Hughes said:
> > I simply ask: when *you* refer to the last ball removed, which ball
> > *is* that?
>
> I am not saying there is a last ball removed. YOU are saying that if you claim
> the vase becomes empty.

No, YOU are saying that the vase being empty implies that
there was a last ball removed, that there was a point
at which the vase had 1 ball.

> That is the point. If you want to claim the vase
> becomes empty, then the onus is upon you to explain how this ball is removed
> and is the last ball, when 10 balls have been added directly before that.

"Directly before" does not have any more meaning for the
infinite sets of insertion and removal times than "last"
does. Your intuition about finite sets, as usual, does not
carry weight on infinite sets.

Look. We have an infinite set of times b_1, b_2, ... < 0,
giving the time that each ball was removed. I claim (as do
the other "Cantorians" in this thread) that if you pick
any t < 0, there are infinitely many b's between t and 0.

Let's imagine sliding t to the right, from negative to
positive. At any given negative value, there are infinitely
many b's to the right of t. When t=0, there are no b's to
the right. They're all to the left.

By your reasoning, there must therefore be an identifiable
time when there is only one b to the right. That simply
isn't true.

- Randy

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