Re: infinitely many nn's = infinite nn's?

On Mar 6, 12:59 am, Phil <toob-head...@xxxxxxxxxxxxx> wrote:
George Dance wrote:
On Mar 5, 5:50 pm, Phil <toob-head...@xxxxxxxxxxxxx> wrote:

G. Frege wrote:

On Mon, 05 Mar 2007 18:01:20 GMT, Phil <toob-head...@xxxxxxxxxxxxx> wrote:

It doesn't. There are infinitely many natural numbers, but each and any is
finite.

I'll agree that this MIGHT _sound_ strange. Maybe the following formulation
is easier to digest:

Each and any natural number is finite.

But the set of _all_ natural numbers is not bound.
(I.e. it does not have an upper boundary.) With other
words, there is no biggest natural number. (I guess
that's immediately clear, no? If W would be this number,
W+1 would be another natural number, but bigger. Which
is an aburdity.)

F.

George, this looks useful and workable; I'll get back to it later!

His name isn't George, BTW. He uses the name "G. Frege" (from Gottlob
Frege, the inventor of predicate logic) as an alias; for all anyone
knows, he may believe that he is Gottlob Frege.

.

Oh, thanks! I was just thinking we have too damn many "Georges" around
here to keep track of, and that will help!-


No problem. Now, just one more bit of help, and I'm outta here. (I
have my own trolls, on my own lists, to battle. 8)


You might have noticed that some of the people "discussing" with you
keep mentioning the name 'Mueckenheim'. That was a new one to me,
since I'd never heard of the guy; but it sounded important, so I
decided to do a search. Much to my surprise I found that he's not the
non-math crank I expected, but a published author. Here's a short
summary of his views, and the information on his book. (I realize
that may be of no use to you now, since you can't read German;
however, translations is a technical business.)

<quote>
Mueckenheim)

My goal is to show that there is no infinity (other than potential
infinity) at all. So we always remain in the finite domain. What
would
be the use of infinite natural numbers? What could you address by oo
=
1 + oo? My goal is to show that set theory is self contradictory, in
particular Cantor's claim of the infinite set of finite naturals.
This
goal is not difficult to achieve. There are several proofs. What is
much more difficult than I ever imagined is to have the set theorists
see and accept them.

By the way, a proof that the irrationals are not uncountable is
already
established by the observation that there is no pair of irrational
numbers which is not separated by a terminating rational number.

Regards, WM </q>
http://sci4um.com/about2-asc-2565.html


Book:
Die Mathematik des Unendlichen
Wolfgang Mückenheim
Shaker Verlag, Aachen, Germany, 2006, ISBN 3-8322-5587-7.





.

Relevant Pages

  • Re: Zero, Infinity
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  • Re: Zero, Infinity
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  • Re: infinitely many nns = infinite nns?
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  • Re: You Dont Have to Be Nuts to Be a Mathematician ...
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