First diagnal proof for real numbers

In his original paper of 1891 G. Cantor does not consider the fact
that dual representation of real numbers can spoil his diagonal proof.
(In fact Cantor treats sequences in general.) Today it is known that
the substitution rule for real numbers in n-ary representation has to
exclude replacement of n-1 by 0 and vice versa. Although E. Zermelo,
the editor of Cantor's collected works, mentioned this already in 1932
(G. Cantor, Gesammelte Werke, p. 280-281) it seems unclear who was the
first to give the correct diagonal proof for real numbers. Regards, WM

.

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