Re: INFINITY Revisited

In article <1126049121.476124.178460@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Don Whitehurst" <whit0911@xxxxxxx> wrote:

> Dave Seaman wrote:
>
> >
> > There is no ball that is added at noon. Noon is simply the
> > earliest time at which we can say all the balls have been added.
> >
>
> Are you then saying that by noon an infinite number of balls have
> been added?
>
> If so, by noon an infinite number of balls have been added: where
> they were added many at a time during each interval and where one
> ball is immediately removed for each of the infinite nth time
> intervals corresponding to the infinite number of naturals.
>
> Clearly, this should be impossible since there is no last natural.
> Similarly there is no time before noon when all of the balls could
> have been added.
>
> Nevertheless, if one assumes that by noon an infinite number of balls
> have been added (where the balls were added many at a time during
> each interval and where one ball was immediately removed for each of
> the infinite nth time intervals (before noon) corresponding to the
> infinite number of naturals associated one each with the removal of
> the balls), I believe it follows that balls with an infinite number
> of digits must also have been added.

Since no natural number has more than finitely many digits in any n-ary
representation, where do those infinitely many digited balls come from?
They cannot come from any natural number!
.

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