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 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
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Re: Diagonalization argument

Quote:
 Originally Posted by mathman If you go straight down, you are changing the first digit over and over again.
(and this doesn't guarantee that you are finding a "new" number)

Quote:
 If you go straight across, you are constructing something different from one number.
(and to show that this new number is not in a given enumeration of the reals in [0, 1), you need to show it's different from ALL the numbers)

 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
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Re: Diagonalization argument

Quote:
 Originally Posted by RandomNumber 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 ?
If the process makes at least one digit of the final number different from each number on the list, it works. If you're using the same up/down-left/right placement I am, that means two right, one down works but one right, two down does not.

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