On Friday, December 6, 2013 4:33:19 AM UTC-7, Albrecht wrote:
> The diagonal argument from Georg Cantor is so silly and easy to destroy. Let's have a "antidiagonal" of all natural numbers. No problem: For any list of naturals we can take the first number and change it by adding 1 to gain d_1, take the second number and, if different from d_1, change it by adding 1 to gain d_2, else d_2:=d_1, and so on. > > For all numbers of the list, the (equivalent to Cantor's antidiagonal) gained antidiagonal d_list is natural (proof: a natural +1 is natural) and different from any number of the list (proof: it is at least 1 more than every number of the list by construction) and thus the list isn't complete. Since this holds for _any_ list of naturals --> the naturals are uncountable.