Cantor diagonalization argument

  • Thread starter arshavin
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sorry for starting yet another one of these threads :p

As far as I know, cantor's diagonal argument merely says-

if you have a list of n real numbers, then you can always find a real number not belonging to the list.

But this just means that you can't set up a 1-1 between the reals, and any finite set.

How does this show there is no 1-1 between reals, and the integers?
 

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  • #2
CRGreathouse
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As far as I know, cantor's diagonal argument merely says-

if you have a list of n real numbers, then you can always find a real number not belonging to the list.
No. It says that if you have a countable list of real numbers, you can form one that isn't anywhere on the list.
 
  • #3
HallsofIvy
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No. It says that if you have a countable list of real numbers, you can form one that isn't anywhere on the list.
Crucial point being "countable" not "n". So there is "no 1-1 between reals, and the integers". Cantor's "list" is not finite.
 

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