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 digits (in the decimal<br>expansion) alternate between odd and even (including the leading 0). Prove that<br>S is uncountable.<br>For instance: 0.1234123412341234... E S while 0.556655665566... E 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: 0.1234123412341234... E S while 0.556655665566... E S

Jun 04, 2022

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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:...

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