Re: infinity

Jesse F. Hughes said:
> "Jesse F. Hughes" <jesse@xxxxxxxxxxxxx> writes:
>
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >
> >> Jesse F. Hughes said:
> >>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >>>
> >>> > Jesse F. Hughes said:
> >>> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >>> >>
> >>> >> > Virgil said:
> >>> >> >> In article <MPG.1d618aae41392f57989fe9@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> >>> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >>> >> >>
> >>> >> >> > > Which ball is not covered by that argument?
> >>> >> >> > N+1 through 10n+9.
> >>> >> >>
> >>> >> >> If TO means "n+1 through 10n+9" he is presuming that there is a last,
> >>> >> >> nth, step, which is specifically prohibited by the rules.
> >>> >> >>
> >>> >> >> And as there is no last step, there is no ball that is not covered.
> >>> >> >>
> >>> >> > Then there is no point at which the last ball is removed. Isn't that
> >>> >> > correct?
> >>> >>
> >>> >> The last ball? What's the number written on that one? When was it
> >>> >> put in?
> >>> > "largest finite. largest finite."
>
>
> Let's take a different approach.
>
> Let's change the problem slightly. Again, we have an infinite set of
> ping pong balls, each ball labeled with a natural number. But instead
> of the old procedure, let's put *all* of the balls into the vase at
> 11:59 and remove the first one. At 11:59:45, we remove the second,
> and so on.
This is the same question Virgil posted a half dozen times in a row.
>
> Tony: Is the vase empty or not at noon?
Yes.
>
> If empty, then when was the last ball removed?
Noon.
>
> If not empty, then which balls did we fail to remove?
None.
>
> Can we put infinitely many balls into a vase by doing it one at a time
> (with increasing speed)? If so, are we able to also empty a vase with
> infinitely many balls by the same method? (Countably infinite in each
> case, of course.)
Yes, but not all countable infinities are the same. This is a basic problem
with "cardinality".
>
>

--
Smiles,

Tony
.

Relevant Pages

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  • Re: infinity
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