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 October 29th, 2011, 09:36 PM #1 Newbie   Joined: Oct 2011 Posts: 7 Thanks: 0 Uncountable Can anyone explain why this function ins't countable? Real #'s with decimal representation of all 1's or all 9's.
 October 30th, 2011, 04:53 AM #2 Member   Joined: Aug 2011 Posts: 85 Thanks: 1 Re: Uncountable These are rational numbers evident by their repeating decimal digits. As a subset of algebraic numbers they are countable. Here is the algorithm to convert any repeating decimal number to a fraction of integers. -a = the initial number -b = No of first unique decimals -c = No of repeating decimals e.g. For a = 3.78123123... we have b = 2 and c = 3 1) Compute d = 10^(b+c) - 10^b 2) Find integer e = d*a 3) The fraction expressing a is then e/d This does not yield the fraction in lowest terms though, but it can be so converted if we know their prime factorization.

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