Re:Gödel's Theorem
by Yajirobe on Thursday January 31, 2019 @05:38AM
(#19043842)
A question about the article. Surely, for any function fn(x) we can just add gn(x) = 1-fn(x) to the table. And so then the argument that there are missing functions does not hold. Why is this reasoning wrong?
[ Parent
| on HN ]
I think you forgot to notice the diagonalization in the article. That is, the newly defined function precisely disagrees with the i-th function when input is i. A similar diagonalization process is used by Cantor to prove the reals are not countable.