Re: An uncountable countable set

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

Why can't we say that every ball that is added is also
removed?
ball #m is added to the vase at time 1/2^(floor(m/10)) minutes
before noon.

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

Every ball is removed before noon, no matter how many
balls there are.

Stephen
.

Relevant Pages

  • Re: An uncountable countable set
    ... The mathematics used in the balls and vase problem ... Each ball is put into the vase at a specific ... Only if you change the order of events, or refuse to say when the vase empties or how. ...
    (sci.math)
  • Re: An uncountable countable set
    ... The mathematics used in the balls and vase problem ... Each ball is put into the vase at a specific ...
    (sci.math)
  • Re: infinity
    ... >>> then the vase is empty. ... The problem is that we can prove every ball put into ... infinity, this esoteric thought experiment is just tossing a match ... mathematics, then mathematics as a human discipline survives. ...
    (sci.math)
  • Re: An uncountable countable set
    ... The only critical time dependency is that each ball to be inserted shall ... the vase is empty at noon of anything of any balls ... An affirmative answer confirms that the vase is empty at noon. ... given the times of insertions and removals. ...
    (sci.math)
  • Re: Questions about the marble problem.
    ... >> a vase and do not remove it then it is still in the vase. ... >> If you put a marble into a vase and then remove it then it ... Not a coincidence at all--by asking a question about time infinity, ... The answer to "is there a ball in the vase ...
    (sci.math)
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