On 2 Mai, 19:51, Dan <dan.ms.ch...@gmail.com> wrote: > On May 2, 11:55 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> You can substitute in any expression "the first digit of 1/9" with > "0.1111....." with "1" and it wouldn't make any difference . > You can substitute all the digit expansions in Cantor's argument with > formulas , and it wouldn't make any difference.
If such expansions exist, that may be possible. But first the digit expansion must be produced in Cantor's list. And that is not possible for self-contradictory expansions. > > In what way you choose to write down the number (whether as a > fraction, or as a digit expansion , etc. ) is of no relevance .
Cantor's argument uses only digits.
> Because it's still THE SAME NUMBER . It still has THE SAME > DIGITS ,even if you can't write them down .
It is not a matter of writing them down. That would be impossible already for a sequence of 10^1000 digits. It is a matter of proving mathematically the non-existence.
Didn't you understand yet the argument? Every power of 10 with natural exponent n can be reflected: 10^n reflected gives 10^-n.
For the infinite sequence 0.111... this is not possible. Therefore it does not exist as sequence of only natural powers of 10. (But supernatural powers are not element of mathematics.)