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Is the following statement true for all irrational numbers α\alpha α:
Consider the set S:={{2nα} ∣ n∈N},S := \big\{\{2^n \alpha\} \, | \, n \in \mathbb{N}\big\},S:={{2nα}∣n∈N}, where {x}\{x\}{x} denotes the fractional part of xxx. Then, SSS is dense in [0,1][0,1][0,1].
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