Problem 3 Let E be the set of all x [0, 1] whose decimal expansion...

Transcribed Image Text:

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] = .a₁a2..an..such that a₁,.., 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. 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] = .a₁a2..an..such that a₁,.., 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.

Answer rating: 100% (QA)

17 E is the contains only If follows possible L set of the ... View the full answer