Re: An uncountable countable set

*** T. Winter wrote:

In article <40ef7$452210c2$82a1e228$23007@xxxxxxxxxxxxxxxx> Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:
...
> 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.

Why the obfuscation? Why not simply Bk = 9 + 9.(k - 1) = 9.k?

Because of the time stamps.

> And that's ALL we can say. The version of the problem used here is
> the first experiment in:

Not only of the first, but also of the second experiment.

Good.

But strange as it may appear, the two experiments give different results.
In the first experiment there is no ball that escapes from being taken
out. In the second experiment there are quite a few balls that are never
taken out. The whole point is that you can not use limits to determine
what is the valid answer.

If you can not use limits to determine what is the valid answer with
infinities, then there _is no_ valid answer. Approaching the infinite
without limits (or rather taking it as a finished thing) demonstrates
how mathematics has become an un-discipline instead of a discipline.

There is nothing "strange as it may appear", or "accepting the counter
intuitive" as with e.g the Theory of Relativity or Quantum Mechanics.
Instead, there's only banality in Cantorian infinitary mathematics.

Han de Bruijn

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