> 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 .