November 1st, 2011, 12:16 PM  #1 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Diagonalization argument
Hi, When working with the diagonalization argument, we construct a function which is different from all other functions in the enumeration by looking at the diagonal. Why dont we walk straight down or right? any reasons? 
November 1st, 2011, 12:24 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  Re: Diagonalization argument
If you go straight down, you are changing the first digit over and over again. If you go straight across, you are constructing something different from one number.

November 1st, 2011, 12:35 PM  #3  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Diagonalization argument Quote:
Quote:
 
November 1st, 2011, 12:38 PM  #4 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Re: Diagonalization argument
Thank you for the response, But how can i visualize whether it works i take two down and one right and then continue? (or) whether it works if i take one down and two right and then continue ? 
November 1st, 2011, 12:40 PM  #5 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Diagonalization argument
Take a look at, for instance, this resource: http://en.wikipedia.org/wiki/Cantor%27s ... l_argument The line "in short, by definition, s_0 is not in the countable sequence S" is key here. Can you guarantee that your method will yield this ^^ result? If so, then you're fine! 
November 1st, 2011, 01:07 PM  #6 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Re: Diagonalization argument
Thank you, I have one more question, List(A), (Where A is enumerable) I just want to know whether the set above is enumerable? 
November 1st, 2011, 01:18 PM  #7 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Diagonalization argument
I don't know what List(A) is.

November 1st, 2011, 01:29 PM  #8 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Re: Diagonalization argument
May be i can say List(enumerable set).

November 1st, 2011, 04:22 PM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Diagonalization argument Quote:
 

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