Closure of the set of irrational number is phi
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http://math.stackexchange.com/questions/283987/interior-closure-and-boundary-of-the-sets-of-all-rational-and-irrational-number
http://math.stackexchange.com/questions/283987/interior-closure-and-boundary-of-the-sets-of-all-rational-and-irrational-number