Re: infinity

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."

Oxymoron. 2nd Peano law states: if n in N -> S(n) in N, so we don't
have a largest finite n.

> If you claim that the vase at some point becomes empty,

Not at some point. After the process completes, which is not the case
after any finite step.

> and want to challenge those that claim otherwise by asking which
> ball remains, then they have equal right to ask which is the final
> ball removed which leaves the vase empty.

There is no final ball removed. After any removed ball, there will be
another ball removed.

> This focus on the names of the balls is entirely unnecessary.

It is necessary because we are dealing with an infinite set, and so
the relation between balls put in and taken out can no longer be
solved without actually looking at the elements, as an infinite set
can be in bijection with a proper subset of itself.

> If you claim the vase is empty at noon, describe the process
> whereby, after growing constantly, the vase is suddenly empty.

Not suddenly. After all steps have completed, which is not the case
after any finite number of steps.

> There is no last ball removed.

Quite so. After _any_ removed ball, more balls will get removed.

> For every ball removed, 10 are added. The vase is never empty,

Not after a finite number of steps.

> and any conclusions to that effect that you derive from this
> retarded Cantorian system indicate assumptions within that system
> which are wrong.

Well, the most awkward leap of faith in the whole construct is that
you indeed can take a look at the results after _all_ steps have been
done.

But you seemed happy enough swallowing that. The actual objections
_you_ bring forward are nonsensical.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

Relevant Pages

  • Re: An uncountable countable set
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  • Re: An uncountable countable set
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  • Re: An uncountable countable set
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  • Re: infinity
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  • Re: infinity
    ... >>> And as there is no last step, there is no ball that is not covered. ... If you claim that the vase at some point becomes empty, ... retarded Cantorian system indicate assumptions within that system which are ...
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