Problem 3 Let E be the set of all x [0, 1] whose decimal expansion...
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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.
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
Posted Date:
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