Question: Problem 3 Let E be the set of all x [0, 1] whose decimal expansion contains only the digits 4 and 7. Prove that

Problem 3 Let E be the set of all x [0, 1] whose decimal expansion contains only the digits 4 and 7. Prove that E is uncountable and a set of measure zero. Hint Consider the set Ej = { [0, 1] = .aa2..an..such that a,.., a, (4,7}}, j = 1,2, ..... Prove that E, and its complement are finite unions of disjoint intervals. Calculate the length of E, and use that E= njej.

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