Re: Cantor and the binary tree

Am 24.05.05 14:58 schrieb mueckenh@xxxxxxxxxxxxxxxxx:

> of paths always equals that of the nodes + 1. It is simply impossible
> to assume that one of these numbers becomes uncountably infinite while
> the other remains countably infinite.

No number can have the property of "being uncountable". What does
that mean? A mathematical concept may require "uncountable many
numbers (or uncountable many of whatever)". So it is "simply
impossible to assume, that one of these numbers becomes uncountably
infinite", I think so; and as well it is impossible, that "the
other remains countably infinite". Even the property of being "countable"
- is commonly used only as a property of an aggregate, not of a single
number (but that may be weakened by freedom of poetry ("i can count on
you"), I think.

Gottfried Helms
.

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