Re: Cantor Confusion


mueckenh@xxxxxxxxxxxxxxxxx wrote:


If there is no bijection with one line, then there must be an element
of the diagonal outside of every line.

No. Not unless the one line
contains every element from every line.

(Because what can be done with
several *finite* lines in their linear order, can be done with one
line).

What can be done with all lines in their linear order
cannot be done with one line.

No, you cannot use the fact that a bijection with one line
must exist to prove that the set of all lines doesn't exist,
then turn around and use the fact the the set of all lines
doesn't exist to prove that a bijection with one line must exist

- William Hughes

.