My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Thanks Tree2Thanks
  • 2 Post By greg1313
Closed Thread
 
LinkBack Thread Tools Display Modes
March 9th, 2018, 08:32 AM   #1
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,363
Thanks: 100

Cantor's Diagonal Argument

Suppose I have a set of all infinite sequences of binary digits.

Either I know the digits of each sequence or I don't.

If I don't, how do I know they are all different?

If I do, I can arrange them in numerical (countable) order. The list has a smallest member 0, and I can decide which of any two members is larger.

Note by moderator: a numerical order doesn't trivially imply countability.

Last edited by skipjack; March 9th, 2018 at 09:41 AM.
zylo is offline  
 
March 9th, 2018, 08:34 AM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,805
Thanks: 1045

Math Focus: Elementary mathematics and beyond
Please continue this discussion here. Thread closed.
Thanks from topsquark and JeffM1
greg1313 is offline  
Closed Thread

  My Math Forum > College Math Forum > Real Analysis

Tags
argument, cantor, diagonal



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Cantor's Diagonal Argument and Infinity zylo Topology 59 May 21st, 2016 07:13 AM
Cantor's Diagonal Argument Reconsidered zylo Topology 12 March 24th, 2016 09:53 AM
Cantor's Diagonal Argument zylo Math 22 January 26th, 2016 08:05 PM
Help! Cantor's Diagonal Argument mjcguest Applied Math 9 July 25th, 2013 07:22 AM
Cantorīs diagonal argument netzweltler Applied Math 191 November 7th, 2010 01:39 PM





Copyright © 2018 My Math Forum. All rights reserved.