Re: An uncountable countable set

stephen@xxxxxxxxxx wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

stephen@xxxxxxxxxx wrote:

Han.deBruijn@xxxxxxxxxxxxxx wrote:

Worse. I have fundamentally changed the mathematics. Such that it shall
no longer claim to have the "right" answer to an ill posed question.

Changed the mathematics? What does that mean?

The mathematics used in the balls and vase problem
is trivial. Each ball is put into the vase at a specific
time before noon, and each ball is removed from the vase at
a specific time before noon. Pick any arbitrary ball,
and we know exactly when it was added, and exactly when it
was removed, and every ball is removed.

Consider this rephrasing of the question:

you have a set of n balls labelled 0...n-1.

ball #m is added to the vase at time 1/2^(m/10) minutes
before noon.

ball #m is removed from the vase at time 1/2^m minutes
before noon.

how many balls are in the vase at noon?

What does your "mathematics" say the answer to this
question is, in the "limit" as n approaches infinity?


My mathematics says that it is an ill-posed question. And it doesn't
give an answer to ill-posed questions.

That is a perfectly reasonable answer. But you do agree that for this problem, the vase is empty at noon for any finite n.
So one wonders what criteria you used to determine that
this infinity cannot be approached via limits.

We can say that the number of balls Bk at step k = 1,2,3,4, ... is:
Bk = 9 + 9.ln(-1/tk)/ln(2) where tk = - 1/2^(k-1) for all k in N .
And that's ALL we can say. The version of the problem used here is
the first experiment in:

http://groups.google.nl/group/sci.math/msg/d2573fcb63cbf1f0?hl=en&;

Han de Bruijn

.

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