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March 4th, 2016, 04:11 PM  #1 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126  Cantors Diag Argument Proves Reals Countable
Let T be the set of all infinite binary series. List all the elements of T and assume the list is uncountable. Use Cantor's Diagonal Argument to show there is a member of T not in the list. Contradiction. Therefore T is countable. 
March 4th, 2016, 04:54 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out.  
March 4th, 2016, 05:01 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,685 Thanks: 2665 Math Focus: Mainly analysis and algebra 
You aren't. Zylo doesn't understand that listing a set and counting a set are the same thing. He does have an irrational desperation to prove Cantor wrong though.

March 4th, 2016, 05:51 PM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,273 Thanks: 943 Math Focus: Wibbly wobbly timeywimey stuff. 
(sighs) Not again! How about this. Make a "list" of T and assume it is countably infinite. Therefore there exists a bijection f from the integers to T. Now use Cantor's diagonal argument to show there is an element of T that is not contained in the already listed elements of T. Therefore f is not onto and thus cannot be a bijection, a contradiction. Therefore T is not countably infinite. Why is this so difficult for you? Dan Last edited by topsquark; March 4th, 2016 at 05:59 PM. 
March 4th, 2016, 06:19 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
I am starting to think that zylo is just posting these as a joke.

March 5th, 2016, 12:44 AM  #6  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
How do you prove that T exists?  
March 5th, 2016, 02:09 AM  #7  
Global Moderator Joined: Dec 2006 Posts: 20,975 Thanks: 2224  Quote:
You've shown that at least one of your assumptions is untenable, but it may be your assumption that all the elements of T can be listed that is false, rather than your assumption that T is uncountable. That means that your argument is unsound (regardless of whether T is countable or uncountable).  

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argument, cantors, countable, diag, proves, reals 
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