Re: infinity
- From: Anon <spamhole@xxxxxxxxxxxxxxxxx>
- Date: Thu, 04 Aug 2005 16:57:36 GMT
On Thu, 04 Aug 2005 09:28:31 -0500, David C. Ullrich
<ullrich@xxxxxxxxxxxxxxxx> wrote:
>On 4 Aug 2005 01:36:00 -0700, snapdragon31@xxxxxxxxx wrote:
>
>>Hi Theo. Before answering your question, I would like to do some math
>>on infinite series first and then explain to you why the vase is not
>>empty at the noon time.
[snip]
>>As seen from the previous example, we cannot just cancel out same terms
>>from each set and come up with result zero. S1 and S2 are infinite
>>series with different properties. We cannot simply say every number in
>>the set S1 also exists in S2 then S1 - S2 = 0. If you do that then you
>>are rearrangeing the numbers in the infinite series.
>
>Reading the start of this post I was all set to reply that it
>was all nonsense. But the fact that the calculations above
>are wrong was exactly your point, great.
>
>>In mathematics, usually if at 'noon' the question is undefined then we
>>would take the limit of the time --> noon to see the tendency of the
>>result
>>As time --> noon
>>S1 = {1, 2, 3, ... , 10n) Number of S1 = 10n
>>S2 = {1, 2, 3, ... , n) Number of S2 = n
>>The remaining balls are {n+1, n+2, ... , 10n}
>># of balls remained in the vase would be n(S1) - n(S2) = 10n - n = 9n >
>>0
>>Therefore, the vase is not empty and actually it is growing rapidly.
>
>Alas, this is wrong. The number of balls in the vase at noon is
>simply not equal to the limit as n -> infinity of the number of
>balls at the n-th stage. It's exactly right that the number of
>balls tends to infinity as we approach noon - it does not follow
>that the vase is not empty at noon. It _is_ empty at noon.
>
The OP has belatedly shared with us that he is talking about the
Littlewood-Ross paradox, and has provided (among other references)
a pointer to a paper by John Byl, ON RESOLVING THE LITTLEWOOD-ROSS
PARADOX at
www.csc.twu.ca/byl/little.fin.doc
[So that no one will have to deal with a .doc file, just Google
'littlewood ross paradox byl' and read the HTML]
Where do you say, if you are, that Byl has it wrong?
>(Which one of the balls does remain at noon, in your opinion?)
>
>>>>From a physical point of view, the number of balls in the vase are
>>growing rapidly as the time approaches noon. Even though, right at
>>the noon time, the problem is undefined but we would expect the vase is
>>not empty.
>
>
>************************
>
>David C. Ullrich
.
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