Re: Cantor Confusion


*** T. Winter schrieb:

> > No, something quite different was argued there. Namely that the limit
> > *also* is the number of edges in the infinite tree (or somesuch)
> > requires transfinite induction.
>
> But is does not.

Indeed, it does not. But I thought you were maintaining that it would be?

Good heavens! I should require transfinite induction?

You need transfinite induction to show that "the number of edges in the
infinite tree" is equal to the limit of "the number of edges in the
finite tree".

No. The number of edges in a finite tree is without interest. We
consider only the infinite tree. The set of edges there can be
enumerated like the set of rational numbers, for instance. If a mapping
N --> Q is defined for every element of Q, then Q is countable. The
mapping N --> {edges} has been established such hat every edge knows
its number.

Regards, WM

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