Date: Fri, 13 Mar 1998 16:14:43 -0500

From: Alex Bogomolny

Abdelilah, hello:

What you want to show is that Cantor's set consists of all fractions that have a representation in the ternary system without digit 1. (There may be two representations but one of them will have this property.)

On the first step, you remove all fractions whose first digit is 1. On the second those whose second digit is one, and so on.

From here it follows that the set is uncountable by the diagonal process or because (replacing 2s with 1s and using now the binary system) there exists a 1-1 correspondence from this set to [0,1].

Best regards,

Alexander Bogomolny