My Math Forum > Math Cardinality of the set of binary-expressed real numbers

 Math General Math Forum - For general math related discussion and news

September 20th, 2018, 05:38 AM   #21
Senior Member

Joined: Dec 2015
From: France

Posts: 103
Thanks: 1

Quote:
 Originally Posted by zylo Is an infinite binary sequence a natural number?
No.

Last edited by skipjack; September 20th, 2018 at 07:59 PM.

 September 20th, 2018, 05:45 AM #22 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 So all natural numbers are finite?
September 20th, 2018, 05:50 AM   #23
Senior Member

Joined: Dec 2015
From: France

Posts: 103
Thanks: 1

Quote:
 Originally Posted by zylo So all natural numbers are finite?
Yes.

Last edited by skipjack; September 20th, 2018 at 08:01 PM.

 September 20th, 2018, 06:09 AM #24 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Clearly we have to define finite. Finite sequence: one that ends I note that the sequence of natural numbers (0,1,2,...) does not end.
 September 20th, 2018, 07:42 AM #25 Senior Member   Joined: Oct 2009 Posts: 912 Thanks: 354 Damn, two Cantor disbelievers arguing with eachother. This is great stuff... Thanks from Maschke
 September 20th, 2018, 08:12 AM #26 Senior Member   Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math $\displaystyle y=1/n$ is simply more dense on $\displaystyle axis$ than $\displaystyle y=n$
September 20th, 2018, 03:06 PM   #27
Senior Member

Joined: Dec 2015
From: France

Posts: 103
Thanks: 1

Quote:
 Originally Posted by zylo Clearly we have to define finite. Finite sequence: one that ends I note that the sequence of natural numbers (0,1,2,...) does not end.
Yes. Infinity means no end in latin.

September 20th, 2018, 08:37 PM   #28
Global Moderator

Joined: Dec 2006

Posts: 21,127
Thanks: 2336

Quote:
 Originally Posted by zylo Clearly we have to define finite.
It suffices to understand "enumeration", "infinitely many" and "infinitely long", as what's being referred to is that any enumeration of infinitely many infinitely long binary sequences allows an infinitely long binary sequence to be specified (by "diagonalization") that isn't in the enumeration.

 September 22nd, 2018, 07:11 AM #29 Banned Camp   Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 It's easy to set up a 1-1 correspondence between infinite binary digits and the natural numbers 0: 00000....... 1: 10000...... 2: 01000...... 3: 11000...... 4: 00100....... 5: 10100....... 6: 01100...... . .
September 22nd, 2018, 07:29 AM   #30
Senior Member

Joined: Oct 2009

Posts: 912
Thanks: 354

Quote:
 Originally Posted by zylo It's easy to set up a 1-1 correspondence between infinite binary digits and the natural numbers 0: 00000....... 1: 10000...... 2: 01000...... 3: 11000...... 4: 00100....... 5: 10100....... 6: 01100...... . .
So what is the natural number associated with 1111111....

(Why am I bothering)

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post topsquark Abstract Algebra 54 August 17th, 2015 08:46 AM Tau Applied Math 4 January 18th, 2014 01:40 PM mente oscura Number Theory 7 June 1st, 2013 03:48 AM farleyknight Applied Math 3 December 20th, 2008 09:01 PM johnny Computer Science 6 October 18th, 2007 11:29 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top