Let F(x) be a non-decreasing function for all x in [0 1], such that
2F(x/3)=F(x) and F(x)+F(1-x)=1
1. Find F(173/1993) and F(1/13).
2. If possible give a general algorithm to find F(x) for any x.
3. Is F(x) uniquely determined(in [0,1])?
4. Is F(x) continuous(in [0,1])?
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Wikipedia: Cantor function
Cut-the-knot: Cantor Set and Function -- A continuous function may grow considerably virtually without changing.
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