Re: Cantor Confusion

In article <1166090945.526859.60550@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:

> You misunderstood. What I explained to *** is another mapping than that
> discussed by us. It is a mapping of one single edge on the path
> representing 1/3, the next edge is mapped on the path representing pi,
> and so on. I claim that for every real number I can name an edge to be
> mapped on this real number.

Yes, you state that, and you can. But that does *not* provide a surjection
from the edges to the real numbers. And you stated you had constructed
such a mapping.

There is a mapping. This is proven by the fact that there are more
edges than paths.

As that "fact" has yet to be proved for infinite trees, you cannot use
it to prove itself.


Perhaps we cannot display it in the special way you
wish. But that is the same with the well ordering of the eals. There
you believe in indirect evidence.

Absent the assumption of the axiom of choice, or something roughly
equivalent, no one claims any well ordering of the reals.

Absent some assumption equivalent to assuming the there are more edges
than paths in a infinite binary tree one cannot prove that there are
more edges than paths. And given such an assumption, one can as easily
prove 2 = 1.


RIght. The disprove is in the fact that whenever I state a sequence of
numbers that sequence inherently does not contain all real numbers.

But the tree does. And the tree does not contain more paths than edges.

That is only true if one assumes it true, it is not deducible from
anything less that its own asssumption.

It is pitty that you cannot combine two thoughts.

It is a pity you cannot combine one.
.

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