How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
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real-analysis
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1To show there exists a number of that form in between any two reals, you could expand them in base 2 and consider the first digit where they're different. – 2011-02-21