In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 30 Apr., 16:23, Dan <dan.ms.ch...@gmail.com> wrote: > > > A real number can be listed by a terminating decimal, by a periodic > > > decimal, or by a formula supplying each of its decimals. > > > > > It is not possible to list irrationals by writing their decimals. > > > Therefore it is not possible to create irrational diagonals of Cantor- > > > lists by writing their decimals. > > > > Let L(n,m) be the m'th decimal of the n'th member of your list of real > > numbers . > > I define A(m) , the m'th decimal of my number , to be > > 2 if L(m,m) not equals 2 , > > or 8 is L(m,m) equals 2 . > > > > Starting from the the fact that a formula for each decimal of every > > number of the list was supplied , I supplied a formula to calculate > > each decimal of my anti-diagonal . My anti-diagonal is well defined, > > and provably not in the list .I didn't write down any digits . > > Read what I wrote: It is not possible to list irrationals by writing > their decimals. Therefore it is not possible to create irrational > diagonals of Cantor-lists by writing their decimals.
While it is not possible to write all digits of an irrational, it is possible, however tedious, to write the nth digit, for any n, which is all that is needed for the diagonal argument.
Thus WM's arguments against the Cantor proof fail again!. --