On 18 Dez., 15:12, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > > Aha, you are clearly a mindreader. Well, as far as I know mindreading > > > is not part of mathematics. Anyhow, I can think of numbers larger than > > > that path. > > > But that is completely irrelevant. I am able to think about a set that > > > contains all natural numbers, you apparently are not. > > > > How do you know that without confirming it by thinking the last too? > > Why need I to think about a last one (which there isn't) to be able to think > about a set that contains all natural numbers? Apparently you have some > knowledge about how my mind works that I do not have.
Yes. A very convincing and often required proof of completenes of a linear set is to know the last element. T talk about all in case there is no last is silly. > > > > > > Right, but there is no finite initial segment that contains them all. > > > > > > > > That is pure opinion, believd by the holy bible (Dominus regnabit in > > > > aeternum et ultra. [2. Buch Moses: Exodus 15 Vers 18]) or forced upon > > > > us by the men-made axiom of infinity. > > > > > > Sorry, I have no knowledge of the bible. But live without that axiom when > > > you can't stomach it. And do not attack mathematicians who live with that > > > axiom. > > > > To live with that axiom does not create uncountability. See the proof > > here: > >http://groups.google.com/group/sci.logic/browse_frm/thread/46fa18c8bb... > > Where is the proof there? I see only you writing a bit of nonsense and two > rebuttals.
One of the rebuttals has meanwhile been changed. Peter Webb recognized: It is true that you cannot show pi as a finite decimal, but you can't show 1/3 as a finite decimal either.
Just what I said. > > > > > The tree contains all paths that can be constructed by nodes, using > > > > the axiom of infinity. Which one would be missing? > > > > > > The infinite paths because you stated a priori that your tree did not > > > contain infinite paths. So it is impossible to construct in your tree > > > infinite paths by the axiom of infinity. > > > > The axiom of infinity establishes the set N from finite numbers. > > It establishes the *existence* of a set N of finite numbers.
What else should be established? > > > It establishes the infinite paths as well in my tree from finite > > paths. > > No. That is impossible because you stated that the paths were finite. > What it *does* establish is the extistence of a set P of finite paths.
It is rather silly to argue about the uncountability of the set of paths. Only minds completely disformed by set theory could try to defend the obviously false position that there were uncountably many paths.
But "10 Questions" will give you the answer why there are not uncountably many paths. There are no infinite decimal expansions of real numbers. There are not due paths in the tree.
It is as impossible to express any real number by an infinite decimal expansion as it is impossible to express 0 by a unit fraction. The rest will be explained in "10 Questions". Therefore I will stop with this topic here.