Cantor diagonalization argument

[arshavin]

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?

 

[CRGreathouse]

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.

 

[HallsofIvy]

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.