Re: Cantor and the binary tree


Robin Chapman wrote:


> >> 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.
>
> "becomes"?

If you prefer "is", you may use it. That does not matter. It is
obviously impossible that the set of paths is uncountable when the set
of nodes is countable, because every pair of paths springs off from one
node, while one path leads to that node. Try to find an error n the
arguing, not in the result.

> One can hardly imagine a simpler mathematical proof. Alas, it's still
> beyond the limits of Chaps

Regards, WM

.

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