So, the following "fact" came up in the topology class I'm helping teach. Lots of people seem pretty sure it's true but I've stared at it for five minutes and can't prove it. Call a rational a "p2" rational if it can be written in the form p/2^n for some prime, p, and natural, n. Given ε >0, can we find a p2 rational in the interval [1/3, 1/3+ ε
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