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Let C be a cantor ternary set

If $x,y \in C,$ then obviously $x-y \in [-1,1]$

Conversely I want to prove that

if $w \in [-1,1],$ then there exists $x,y \in C$ such that $x-y=w$

How to prove this problem?

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    a) Are you aware of the practice of accepting answers? b) You can't prove a problem; you prove statements, assertions, theorems, ...2012-09-19

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