April 27th, 2017, 08:59 AM  #11 
Senior Member Joined: Dec 2015 From: Earth Posts: 232 Thanks: 26 
$\displaystyle A\rightarrow$ not absolutely $\displaystyle A$

April 27th, 2017, 11:13 AM  #12  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,327 Thanks: 2451 Math Focus: Mainly analysis and algebra  Quote:
(2) So what, false, false. The irrational numbers are by definition the limit of sequences of rationals.  
April 27th, 2017, 12:30 PM  #13 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100 
The LIMIT of an infinite binary digit is a real number. Cantor does not consider the set of limits of infinite binary digits, he considers the set of infinite binary digits, which are rational numbers, which are countable. 
April 27th, 2017, 12:35 PM  #14 
Senior Member Joined: Aug 2012 Posts: 1,956 Thanks: 547  That's absurd. Each item on the list is a real number, an infinite decimal or binary sequence. What on earth are you talking about? You sound bored. You haven't even got an argument.

April 27th, 2017, 12:49 PM  #15 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,327 Thanks: 2451 Math Focus: Mainly analysis and algebra  
April 28th, 2017, 05:33 AM  #16  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100  Quote:
Quote:
A binary sequence is a natural number. An infinite binary sequence is a natural number. The natural numbers are countable. CDA is wrong. Last edited by zylo; April 28th, 2017 at 05:39 AM.  
April 28th, 2017, 05:43 AM  #17 
Global Moderator Joined: Dec 2006 Posts: 19,163 Thanks: 1638  
April 28th, 2017, 05:47 AM  #18 
Senior Member Joined: Aug 2012 Posts: 1,956 Thanks: 547  
April 28th, 2017, 06:20 AM  #19  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,390 Thanks: 100  Quote:
101010......... makes no sense if there is a largest natural number. Do you happen to know what it is? Presumably all binary digits of an infinite binary sequence are known, otherwise it would make no sense to speak of AN infinite binary sequence.  
April 28th, 2017, 06:56 AM  #20  
Senior Member Joined: Aug 2012 Posts: 1,956 Thanks: 547  Quote:
 

Tags 
argument, cantors, diagonal, logic 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cantors Diagonal Argument is Not Diagonal  v8archie  Topology  0  June 23rd, 2016 09:16 AM 
Cantors Diagonal Argument and Epimenides  zylo  Topology  4  March 8th, 2016 06:08 AM 
Cantors Diag Argument Proves Reals Countable  zylo  Topology  6  March 5th, 2016 02:09 AM 
Cantor's Diagonal Argument  zylo  Math  22  January 26th, 2016 08:05 PM 
Cantorīs diagonal argument  netzweltler  Applied Math  191  November 7th, 2010 01:39 PM 