Re: Relative Cardinality

mueckenh@xxxxxxxxxxxxxxxxx wrote:
> Do you really think it necessary to demonstrate such things here?
> Recently we had a proof that sqrt(2) is not rational. We should
> concentrate on more general problems: It is impossible to label more
> than 10^100 entities by all particles the univese supplies. Therefore
> there cannot exist a set with more than 10^100 elements and we cannot
> count up to 10^10^100.

Ahh, your wonderful "sets can only be represented by particles in the
universe" theory. Did you ever notice that mathematicians work with
stuff "in principle" not "in reality." Sets are IDEAS not some
particles in the universe. That is, mathematics should not change if
we realize suddenly that all our ideas about the universe were wrong.
I think you might be wanting to post in sci.physics, not sci.math.

Did you also ever notice that our entire theory that the universe is
finite is based on theories that are based on mathematics that assume
the reals are a continuum (that is complete, that is uncountable?)

If you restrict yourself to finitistic mathematics, then you have no
way of actually predicting that the universe is finite, so you get into
a twilight zone where the universe could be infinite, and your argument
against infinite sets could be wrong, but then we could use those
infinities to predict that the universe is finite and those infinities,
after serving us for so long would go "poof" because the universe is
finite?

I also thought of another irrational number that escapes your logic.
Take the number:
0.9909000900000009000... That is the number whose digital
representation has 9s in the places that are powers of 2. It is the
"sum(n=0 to oo) 9*10^(-(2^n))". So then I can say what the 10^10^100's
digit is, it is 0. Also the 2^100^100^100^100^100^100^100^100's digit
is 9. And the next digit after that is 0. I wonder why this number
doesn't exist and why it cannot be on any list.

Jiri

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