Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx wrote:

MoeBlee schrieb:


This number does not exist. The diagonal has not omega positions.

So I guess the answer to my question is that you are not prepared to
show that my proof has anything more than first order logic applied to
Z set theory nor are you prepared to demonstrate a contradiction in Z
set theory.

Your proof shows either a contradiction in Z or it shows that Z is
false.

Z contains a contradiction to your proof, if one can show in Z that a
diagonal of a matrix has not more elements than every line. Z is false,
if one cannot show that. So, why further bother about Z?

It appears you are mislead by your loose terminology.

In a finite square matrix, the length of the diagonal equals the height
and the width, e.g.,


1 2 3
4 5 6
7 8 9

However, why should the diagonal of a triangle with infinite height be
the same length as one of its lines? You have claimed this, but you have
not explained why you believe this to be true. Looking at the following
picture, it seems to be obviously false.

1
2 3
4 5 6
7 8 9 10
....

The length of the diagonal is clearly the same as the length of the
first column. And, the first column "goes on forever", while each line
does not "go on forever".

What is wrong with my reasoning?

--
David Marcus
.

Relevant Pages

  • Re: Cantor Confusion
    ... And, the first column "goes on forever", while each line ... "It goes on forever" does not mean actually infinite length. ... Why should something that is clear from the picture be ...
    (sci.math)
  • Re: Cantor Confusion
    ... or equal to the length of the first column. ... For a diagonal longer than every line this ... You make an assertion, but you do not give a proof of that assertion. ... Neverheless it is a contradiction. ...
    (sci.math)
  • Re: Cantor Confusion
    ... And, the first column "goes on forever", while each line ... What is wrong with my reasoning? ... David Marcus ...
    (sci.math)
  • Re: OT for those interested in arguments
    ... Either that or just listen to the Monte Python Argument sketch. ... "That's not an argument, that's just contradiction." ... Forever { ...
    (rec.models.railroad)
  • Re: OT for those interested in arguments
    ... Either that or just listen to the Monte Python Argument sketch. ... "That's not an argument, that's just contradiction." ... Forever { ...
    (rec.models.railroad)