October 29th, 2011, 10:36 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, 05:53 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. 

Tags 
uncountable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
show that M is uncountable  450081592  Real Analysis  2  November 23rd, 2011 07:34 PM 
Prove that f: N > {0,1} is uncountable  arcdude  Applied Math  1  November 23rd, 2011 12:46 PM 
countable, uncountable  wannabe1  Real Analysis  5  September 22nd, 2010 04:18 PM 
Surjection, Uncountable Set  vaevictis59  Applied Math  18  March 16th, 2010 10:14 AM 
Sets, Countable and Uncountable  Bernie  Applied Math  3  September 9th, 2009 02:28 AM 