Re: Cantor and the binary tree

In article <1119733280.288461.40120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
> *** T. Winter wrote:
> > > Theorem. Any set of even numbers has a cadinality which is less than
> > > infinite.
> > > Proof 2n > Card({2,4,6,...,2n}).
> > >
> > > If the set of all even numbers should have a larger cardinal number
> > > than any finite natural, then beyond the last one, 2n,
> >
> > In the set of all even numbers there is no last one.
>
> But the numbers there are all finite even numbers, for which my theorem
> holds. I am glad that there is no last one which could spoil my proof.
> The proof is based on the fact, that there is always another one (but
> a finite natural, of course).
>
> The proof, using complete induction, does not work for a last one. But
> it works for any one.

Yes, for any finite number, so the set on the right hand side is always
finite and the number on the left hand side is always inite and the last
element of the set on the right hand side. Your induction will not get
you the set of all even numbers on the right hand side, because what
should be on the left hand side? So how you can get to your conclusion
for the set of all even numbers using induction?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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