Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:

> Jesse F. Hughes said:
>>
>> I wonder if the following scenario is slightly more palatable to Tony
>> and crew.
>>
>> 11:59 Put an unlabeled ball in.
>> 12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
>> in. Take out ball n.
>> 12:00 Take out the unlabeled ball.
>>
>> Claim: The vase is empty at 12:00:01. The last ball taken out was the
>> only unlabeled ball put it.
>>
>> Proof of claim: One ball put in was unlabeled, but it was removed at
>> 12:00.
>>
>> Each other ball put in was labeled with some number k. It was put in
>> prior to 12:00 - 2^(-k) and was removed at 12:00 - 2^(-k). Thus,
>> there are no labeled balls in the vase at noon.
>>
>> It is a trivial change to the problem, but it should take away the
>> silly complaint that a vase can only be empty if the "last" ball is
>> removed.
>>
>> Of course, the same could be done by a simpler fix:
>>
>> 12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
>> in. Take out ball n + 1.
>> 12:00 Take out ball 1.
>>
> I'm sorry, but that really doesn't help any.

What a remarkably utterly unthoughtful reply.

Half the time, you claim that the vase can't be empty because we never
remove a "last ball"[1]. So, I fix it so that we remove a last ball.
How can you complain?

Is it that we didn't remove a second-to-last? And third-to-last? No
sweat. I'll fix it some more.

12:00 - 2^(-n) min. Put balls 10*n - 9, 10 * 9 - 8, ..., 10 * n
in. Take out ball 2n.
12:00 + 2^(-n) min Take out ball 2n - 1.

How about that? Now we remove a first, second, third ball...
and at noon we start removing the ... fourth from last, third from
last, second from last and last ball. Now surely the vase is empty.

Right, Tony?

Footnotes:
[1] Of course, you say about another thought experiment that the vase
*is* empty even though there is no last ball removed.

--
"Even if [...] a communistic regime should come [to China], the old
tradition [...] will break Communism and change it beyond recognition,
rather than Communism [...] break the old tradition. It must be so."
-- Lin Yutang on "Socialism with Chinese characteristics" in 1935
.

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: An uncountable countable set
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  • Re: infinity
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