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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