April 27th, 2017, 09:59 AM  #11 
Senior Member Joined: Dec 2015 From: Earth Posts: 337 Thanks: 44 
$\displaystyle A\rightarrow$ not absolutely $\displaystyle A$

April 27th, 2017, 12:13 PM  #12  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,572 Thanks: 2568 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, 01:30 PM  #13 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,648 Thanks: 119 
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, 01:35 PM  #14 
Senior Member Joined: Aug 2012 Posts: 2,141 Thanks: 623  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, 01:49 PM  #15 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,572 Thanks: 2568 Math Focus: Mainly analysis and algebra  
April 28th, 2017, 06:33 AM  #16  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,648 Thanks: 119  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 06:39 AM.  
April 28th, 2017, 06:43 AM  #17 
Global Moderator Joined: Dec 2006 Posts: 20,117 Thanks: 1912  
April 28th, 2017, 06:47 AM  #18 
Senior Member Joined: Aug 2012 Posts: 2,141 Thanks: 623  
April 28th, 2017, 07:20 AM  #19  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,648 Thanks: 119  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, 07:56 AM  #20  
Senior Member Joined: Aug 2012 Posts: 2,141 Thanks: 623  Quote:
 

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