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October 4th, 2018, 11:42 AM  #1  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,603 Thanks: 115  Cantor's Diagonal Argument is Wrong
This is a slight refinement (simplification and condensation) of my previous expositions which evolved in the quoted thread. I put it here because it was being buried, and because it addresses the subject directly. Quote:
 
October 4th, 2018, 11:46 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,888 Thanks: 1836 
As I stated before, it's unclear and incorrect.

October 4th, 2018, 11:51 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
I thought we'd agreed to close down this sort of idiocy.

October 4th, 2018, 12:04 PM  #4 
Senior Member Joined: May 2016 From: USA Posts: 1,192 Thanks: 489  It is also irrelevant. No one, particularly not Cantor, said that you could not represent all the natural numbers by an infinite list of infinite bit strings. What he proved was that, if you accept the idea of infinite strings and infinite lists at all, any infinite list that can be placed in onetoone correspondence with the natural numbers will be incomplete. Zylo's intuition is that this idea is ridiculous. Consequently, he assumes that such a list is complete. But an assumption is not a proof. He does everything in the world except address Cantor's argument. There are two plausible responses to Cantor. One is to reject the idea that the infinite "exists" and therefore to adopt the position that theorems about infinity have the same epistemological status as theorems about the psychology of werewolves. The other is to accept that, at least in the human imagination, the infinite exists but follows rules that are completely alien to human intuition. 
October 4th, 2018, 12:05 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,888 Thanks: 1836 
We don't need this as a separate thread for the time being, so I've closed it. I might ultimately reopen it by transferring all the related posts from the other thread.


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