Let S be the subset of (0, 1) consisting of numbers whose digits (in the decimal expansion) alternate between odd and even (including the leading 0). Prove that S' is uncountable. For instance:...


Let S be the subset of (0, 1) consisting of numbers whose<br>digits (in the decimal expansion) alternate between odd and<br>even (including the leading 0). Prove that S' is<br>uncountable.<br>For instance: 0.123412341234123... E S while<br>0.556655665566... ¢ S<br>

Extracted text: Let S be the subset of (0, 1) consisting of numbers whose digits (in the decimal expansion) alternate between odd and even (including the leading 0). Prove that S' is uncountable. For instance: 0.123412341234123... E S while 0.556655665566... ¢ S

Jun 04, 2022
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