Re: Cantor and the binary tree



*** T. Winter wrote:
> There is a
> distinction between "the set is not infinite" and "none of the elements
> is infinite".

And just this distinction is wrong for ordered sets where every element
has an initial segment.

What does it mean, that every number is finite?
It means that the belonging initial segment is finite, for *every*
number.
The limit n --> omega is not taken in N as 0 is not taken by any 1/n.

Sets like N are potentially infinite but never actually infinite.

{1,2,3,...,omega} would be actually infinite, but it would not be
countable, because we cannot count beyond n e N.

Regards, WM

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