On 1 Mai, 23:31, Dan <dan.ms.ch...@gmail.com> wrote:
> > Yes, that is true. But (and please read this very attentively!): > > Cantor's argument requires the existence of the complete sequence > > 0.111.... in digits: > > > You can see this easily here: > > > The list > > > 0.0 > > 0.1 > > 0.11 > > 0.111 > > ... > > > when replacing 0 by 1 has an anti-diagonal, the FIS of which are > > always in the next line. So the anti-diagonal is not different from > > all lines, unless it has an infinite sequence of 1's. But, as we just > > saw, this is impossible. > > I see no significant difference between referring to a mathematical > object by a formula and referring to it by 'writing it down' .
But Cantor's argument is invalid, in this special case, unless it can produce 0.111... with actually infinitely many 1's, i.e. more than every finite number of 1's.
It does not matter whether 1/9 exists as a fraction or whether it exísts in the ternary system as 0.01. In order to differ from every entry of my list Cantor's argument needs to produce, digit by digit, the infinite sequence. And that does not exist.