My Math Forum Cantor's Diagonal Argument and Infinity

 Real Analysis Real Analysis Math Forum

 March 19th, 2018, 03:22 PM #1 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 Cantor's Diagonal Argument and Infinity If infinity means endless, you can never get to the end of CDA.
 March 19th, 2018, 03:52 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 There's no "end" of the integers, either. Thanks from topsquark
 March 19th, 2018, 03:53 PM #3 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,073 Thanks: 843 Math Focus: Wibbly wobbly timey-wimey stuff. Or business meetings. -Dan Thanks from Benit13, JeffM1 and SDK
March 19th, 2018, 04:07 PM   #4
Senior Member

Joined: Oct 2009

Posts: 752
Thanks: 257

Quote:
 Originally Posted by zylo If infinity means endless
It doesn't though...

March 19th, 2018, 04:14 PM   #5
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 124

Quote:
 Originally Posted by zylo If infinity means endless, you can never get to the end of CDA.
Infinity, infinite, and endless are synonymous. But if it makes you happy:

If infinite means endless, you can never get to the end of CDA.

March 19th, 2018, 04:20 PM   #6
Senior Member

Joined: Oct 2009

Posts: 752
Thanks: 257

Quote:
 Originally Posted by zylo Infinity, infinite, and endless are synonymous.
The ordinal $\omega+1$ has an end and is infinite.

 March 19th, 2018, 04:43 PM #7 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124 An increasing sequence of Natural numbers either ends (finite), or doesn't (infinite), 1,2,3 is a finite sequence (ends) 1,2,3,4........ is an infinite sequence (endless)
March 19th, 2018, 04:50 PM   #8
Senior Member

Joined: Oct 2009

Posts: 752
Thanks: 257

Quote:
 Originally Posted by zylo An increasing sequence of Natural numbers either ends (finite), or doesn't (infinite), 1,2,3 is a finite sequence (ends) 1,2,3,4........ is an infinite sequence (endless)
Sure, and there are also infinite sets which do end.

March 19th, 2018, 04:58 PM   #9
Banned Camp

Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 124

Quote:
 Originally Posted by Micrm@ss Sure, and there are also infinite sets which do end.
Please give an example of an infinite sequence of binary digits which ends.

March 19th, 2018, 05:32 PM   #10
Senior Member

Joined: Oct 2009

Posts: 752
Thanks: 257

Quote:
 Originally Posted by zylo Please give an example of an infinite sequence of binary digits which ends.
The ordinal $\omega +1$

 Tags argument, cantor, cantors, diagonal, infinity

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post zylo Real Analysis 1 March 9th, 2018 08:34 AM zylo Topology 147 August 14th, 2016 07:40 PM zylo Topology 59 May 21st, 2016 07:13 AM zylo Math 22 January 26th, 2016 08:05 PM netzweltler Applied Math 191 November 7th, 2010 01:39 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top