Re: Cantor Confusion

In article <1163073873.832639.10700@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

MoeBlee schrieb:



As I said, I don't care about (3).

My mathematical notions include the fact that the diagonal of a matrix
cannot have more elements than every line. If in your opinion this
position is not valid in ZFC or in your logic, then we should stop
here.

WM should certainly stop here, as his claim is just plain silly.

If the nth line contains at least n positions but is still finite then
the diagonal will be at least as long as every finite line, thus will be
longer that any finite line which is not a last line.

But if the lines correspond to the members of N, there cannot be a last
line.

Conclusion: The diagonal is longer than every finite line.

To argue otherwise is to ignore the facts.


since I would not have bothered to even post
a proof about denumerable sequences and talk with you about it for so
long if I accepted any condition that I can't use the axiom of
infinity.

That is *not my condition* but it is the result which follows from the
fact that the diagonal cannot be longer than every line.

It can be as long as every finite line, and longer that all but the
longest, if there were one.

Thus if there is no longest or infinitely long line, the diagonal is
longer that all lines.




If I have the
choice either to accept the axiom of infinity with the condition that a
diagonal can be longer than every line, or to drop both notions, then I
choose the second.

A stupid choice, but each person has the right to go to hell in his own
way.




If you can live with the contrary, then try to do
it. I wish you nice dreams.

Not to worry, our dreams are better than yours.
.