Something dynamics can tell us about number theory

A family of functions

We shall use a family of functions f2, f3, f4, f5, ..., all with domain and range [0, 1].
Here are the graphs of the first three.
f2 f3 f4
For example, f2(x) =
2xfor 0 ≤ x < 1/2
2x - 1for 1/2 ≤ x ≤ 1

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