Re: infinity

On 5 Aug 2005 15:37:47 -0700, snapdragon31 wrote:
> The original question:
> Problem 1
> Suppose you have a giant vase and a bunch of ping pong balls with an
> integer written on each one, e.g. just like the lottery, so the balls
> are numbered 1, 2, 3, ... and so on. At one minute to noon you put
> balls 1 to 10 in the vase and take out number 1. At half a minute to
> noon you put balls 11 - 20 in the vase and take out number 2. At one
> quarter minute to noon you put balls 21 - 30 in the vase and take out
> number 3. Continue in this fashion. Obviously this is physically
> impossible, but you get the idea. Now the question is this: At noon,
> how many ping pong balls are in the vase?

> We can change the above question into an equivalent problem.
> Problem 2.
> Suppose you have a giant vase and a bunch of ping pong balls with an
> integer written on each one, e.g. just like the lottery, so the balls
> are numbered 1, 2, 3, ... and so on.
> At minute 1 you put balls 1 to 10 in the vase and take out number 1.
> At minute 2 you put balls 11 - 20 in the vase and take out number 2.
> At minute 3 you put balls 21 - 30 in the vase and take out number 3.
> Continue in this fashion. Obviously this is physically impossible, but
> you get the idea. Now the question is this: At an infinite time from
> now, how many ping pong balls are in the vase?

> William Hughes wrote:
>> > According to this problem, noon is not reachable.

>> Wrong. The experiment described is quite well defined. We know
>> which balls are added to the vase and when and we can consider
>> the different outcomes by choosing which balls are removed from
>> the vase and when. Noon is not reachable in any physical sense,
>> but we know that the experiment described has no physical realization
>> or approximation.

> I hope you can see that 'noon' in problem 1 is equivalent to 'an
> infinite time from now' in problem 2. They are un-reachable. Again I
> have to emphasis that in order to prove the vase is empty, we have to
> prove that the last ball is taken out from the vase.

Noon may be un-reachable in a physical sense, but this is not a physical
problem. It's a mathematical problem. The question makes perfect sense
from a mathematical standpoint.

Your final sentence above makes no sense at all. There is no such thing
as a "last ball". All that is necessary to show that the vase is empty
is to show that each ball is removed from the vase before noon and is not
subsequently replaced.

> Assume f(x) is an increasing function and f(0) > 0. Even though f(oo)
> is undefined but I am quite sure that f(oo) cannot be 0.

Why?


--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
.

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