In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
But no expansion beyond a finite number of decimal or other base places is ever needed, and that is at least theoretically possible for any real that can be named well enough to be listed at all. > > > > 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.
But can you name a real for which an n-place approximation is theoretically impossible? Unless yo can, Cantor wins!
> Didn't you understand yet the argument? Every power of 10 with natural > exponent n can be reflected: 10^n reflected gives 10^-n.
True, but totally irrelevant to the Cantor theorem which WM is so vainly protesting against. --