My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum


Thanks Tree9Thanks
Reply
 
LinkBack Thread Tools Display Modes
April 27th, 2017, 08:59 AM   #11
Senior Member
 
Joined: Dec 2015
From: Earth

Posts: 154
Thanks: 21

$\displaystyle A\rightarrow$ not absolutely $\displaystyle A$
idontknow is offline  
 
April 27th, 2017, 11:13 AM   #12
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,940
Thanks: 2266

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by zylo View Post
Ref previous post.
(1) is CDA, the subject of this thread. You can't use CDA to prove CDA.

(2) Each a_{n} is a rational number.
Any rational combination of rational numbers is a rational number.
The rational numbers are countable.
(1) CDA is a proof. It's not something that requires proof. The uncountability of (non-terminating, non-repeating) sequences of decimal digits doesn't require CDA.
(2) So what, false, false. The irrational numbers are by definition the limit of sequences of rationals.
v8archie is offline  
April 27th, 2017, 12:30 PM   #13
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,134
Thanks: 88

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.
zylo is offline  
April 27th, 2017, 12:35 PM   #14
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by zylo View Post
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.
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.
Maschke is offline  
April 27th, 2017, 12:49 PM   #15
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,940
Thanks: 2266

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by zylo View Post
The LIMIT of an infinite binary digit is a real number
Nonsense. A binary digit isn't even a sequence. A sequence isn't a number. The CDA doesn't make any reference at all to numbers. It's a proof about sequences, not limits of sequences.
v8archie is offline  
April 28th, 2017, 05:33 AM   #16
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,134
Thanks: 88

Quote:
Originally Posted by Maschke View Post
I don't know what that means. 3 + 1/10 + 4/100 + 1/1000 + ... is a combination of rational numbers that sums to $\pi$.

Please make your posts self-contained if you want people to respond.
It's limit is pi, but it never equals pi. Just like Lim 1/n is zero but 1/n never equals 0. CDA is not about limits, it is about sequences.

Quote:
Originally Posted by v8archie View Post
Nonsense. A binary digit isn't even a sequence. A sequence isn't a number. The CDA doesn't make any reference at all to numbers. It's a proof about sequences, not limits of sequences.
CDA allegedly proves the real numbers are countable (put a period before each one).

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.
zylo is offline  
April 28th, 2017, 05:43 AM   #17
Global Moderator
 
Joined: Dec 2006

Posts: 17,919
Thanks: 1385

Quote:
Originally Posted by zylo View Post
An infinite binary digit is a natural number.
No, it's not a natural number.
skipjack is offline  
April 28th, 2017, 05:47 AM   #18
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by zylo View Post
An infinite binary sequence is a natural number.
What natural number is .10101010101010101010101010..., with or without the binary point?
Maschke is offline  
April 28th, 2017, 06:20 AM   #19
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,134
Thanks: 88

Quote:
Originally Posted by Maschke View Post
What natural number is .10101010101010101010101010..., with or without the binary point?
$\displaystyle p=a{_n}2{^n}+......+a_{1}2{^1}+a{_0}2{^0}$

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.
zylo is offline  
April 28th, 2017, 06:56 AM   #20
Senior Member
 
Joined: Aug 2012

Posts: 1,527
Thanks: 364

Quote:
Originally Posted by zylo View Post
$\displaystyle p=a{_n}2{^n}+......+a_{1}2{^1}+a{_0}2{^0}$

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.
You've lapsed into utter incoherence.
Maschke is offline  
Reply

  My Math Forum > College Math Forum > Topology

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





Copyright © 2017 My Math Forum. All rights reserved.