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Topic: Matheology § 285
Replies: 84   Last Post: Jun 15, 2013 6:05 PM

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 Ralf Bader Posts: 488 Registered: 7/4/05
Re: Matheology § 285
Posted: Jun 11, 2013 7:06 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Tuesday, 11 June 2013 20:43:30 UTC+2, Zeit Geist wrote:
>

> > I think your algorithm fails at the limit stage.
>
> That's the same with enumerating the rationals and with the diagonal of
> the list. No limits available in all these cases.
> If we enumerate the rationals, we do it up to n (since there is no
> infinite natural number).

No. Maybe you try to do it so, because you are stupid. WE might do something
like this: We note that a positive rational r can be written as
r = p_1^n1 * p_2^n2 * ... * p_k^nk, i.e. a product of powers of primes p_i
with integer exponents ni. And then we map r to p_1^f(n1) * p_2^(n2) * ...
* p_k^f(nk), where f(n) = 2n if n>0 and f(n) = -2n-1 if n<0 or so. We take
some care with the cases r=0, r=1, ni=0 and then we can show that we have
got a bijection from the positive rationals to the naturals.

There is nothing WE do "up to n". There is no limit involved. What we need
are variables ranging over various sets of numbers. I don't know whether a
set of numbers must "actually exist" in order to be allowed to use
variables ranging over that set.

point. For example
is anything but convincing. There one reads:
"2. The universe began to exist.

2.1 Argument based on the impossibility of an
actual infinite.

2.11 An actual infinite cannot exist.
2.12 An infinite temporal regress of
events is an actual infinite.
2.13 Therefore, an infinite temporal
regress of events cannot exist. "
Then some arguments for the alleged non-existence of an actual infinite are
derived from Hilbert's hotel. But this is completely beyond the point,
those arguments at best saying that the events in that infinite regress can
not be shuffled around like the guests in that hotel. And indeed they
can't, because they are in a fixed order and no events can b checked in or
out of the past. (But even if the arguments given for the non-existence of
actual infinities would apply, they still would not be convincing.)

Talking about the infinite in that way is totally empty. The differences are
in what one can do with that infinite. For example, using variables ranging
ove the set of natural numbers. Or show the existence of a natural number
with certain properties by contradiction - this requires much more "actual
existence" of the set of naturals than merely using variables. In
mathematics we at least implicitly know this. You don't, because you are
too stupid for mathematics.

Date Subject Author
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 JT
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/14/13 Virgil
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Scott Berg
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Virgil
6/11/13 Tanu R.