My Math Forum  

Go Back   My Math Forum > Math Forums > Math

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


Thanks Tree9Thanks
Reply
 
LinkBack Thread Tools Display Modes
September 20th, 2018, 04:38 AM   #21
Member
 
Joined: Dec 2015
From: France

Posts: 78
Thanks: 1

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

Last edited by skipjack; September 20th, 2018 at 06:59 PM.
Pengkuan is offline  
 
September 20th, 2018, 04:45 AM   #22
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,529
Thanks: 107

So all natural numbers are finite?
zylo is offline  
September 20th, 2018, 04:50 AM   #23
Member
 
Joined: Dec 2015
From: France

Posts: 78
Thanks: 1

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

Last edited by skipjack; September 20th, 2018 at 07:01 PM.
Pengkuan is offline  
September 20th, 2018, 05:09 AM   #24
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,529
Thanks: 107

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.
zylo is offline  
September 20th, 2018, 06:42 AM   #25
Senior Member
 
Joined: Oct 2009

Posts: 544
Thanks: 174

Damn, two Cantor disbelievers arguing with eachother. This is great stuff...
Thanks from Maschke
Micrm@ss is online now  
September 20th, 2018, 07:12 AM   #26
Senior Member
 
Joined: Dec 2015
From: Earth

Posts: 245
Thanks: 27

$\displaystyle y=1/n $ is simply more dense on $\displaystyle axis$ than $\displaystyle y=n$
idontknow is offline  
September 20th, 2018, 02:06 PM   #27
Member
 
Joined: Dec 2015
From: France

Posts: 78
Thanks: 1

Quote:
Originally Posted by zylo View Post
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.
Pengkuan is offline  
September 20th, 2018, 07:37 PM   #28
Global Moderator
 
Joined: Dec 2006

Posts: 19,700
Thanks: 1804

Quote:
Originally Posted by zylo View Post
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.
skipjack is offline  
September 22nd, 2018, 06:11 AM   #29
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,529
Thanks: 107

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......
.
.
zylo is offline  
September 22nd, 2018, 06:29 AM   #30
Senior Member
 
Joined: Oct 2009

Posts: 544
Thanks: 174

Quote:
Originally Posted by zylo View Post
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)
Micrm@ss is online now  
Reply

  My Math Forum > Math Forums > Math

Tags
binaryexpressed, cardinality, continuum hypothesis, diagonal argument, numbers, real, set



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Cardinality of transcendental numbers topsquark Abstract Algebra 54 August 17th, 2015 07:46 AM
How does cardinality apply to real numbers? Tau Applied Math 4 January 18th, 2014 12:40 PM
Powers expressed as sum of consecutive numbers mente oscura Number Theory 7 June 1st, 2013 02:48 AM
Cardinality of the Real numbers farleyknight Applied Math 3 December 20th, 2008 08:01 PM
Binary Numbers johnny Computer Science 6 October 18th, 2007 10:29 AM





Copyright © 2018 My Math Forum. All rights reserved.