February 4th, 2016, 07:48 PM  #21 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203  That's simply incorrect, as the phrase "all natural numbers" doesn't mean "from 1 to infinity". The article you linked to doesn't use the word "infinity". It refers to "all values of $n$". There are infinitely many possible values of $n$, but none of them is "infinity". 
February 4th, 2016, 07:48 PM  #22  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126  Quote:
https://en.wikipedia.org/wiki/Mathematical_induction For those who don't like or understand my proofs that the reals are countable, there is a "proof" that the reals are uncountable: https://en.wikipedia.org/wiki/Cantor...tability_proof Take your choice.  
February 4th, 2016, 07:53 PM  #23 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
There is no such choice, as your assertions rely on a phrase that doesn't appear in the article you linked to. The linked article doesn't use the word "infinity".

February 4th, 2016, 07:53 PM  #24  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra  Quote:
Quote:
Everyone else here both knows and understands Cantor's proof. It's, again, just you that doesn't. Last edited by skipjack; February 4th, 2016 at 07:58 PM.  
February 4th, 2016, 09:35 PM  #25  
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244  Quote:
$$\aleph_0\in\mathbb{N},$$ Or maybe just $$\infty\in\mathbb{N}.$$  
February 5th, 2016, 06:55 AM  #26 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126  Do you believe in the principle of mathematical induction?
Last edited by skipjack; February 5th, 2016 at 07:25 AM. 
February 5th, 2016, 07:19 AM  #27 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
The principal of mathematical induction is not like Father Christmas. It's a method that exists by logical deduction, not a story that you can choose to believe or not. If it were a story, you could make up whatever conclusion you wanted, but since it's not, you can't  which is something you don't seem to be able to come to terms with. Last edited by skipjack; March 5th, 2016 at 11:31 AM. 
February 5th, 2016, 07:26 AM  #28 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203  You've already provided a link for mathematical induction, and the linked article doesn't use the word "infinity", so your proofs using induction and claiming to show that the reals are countable only show that terminating decimals are countable, which excludes all irrational reals.

February 5th, 2016, 08:15 AM  #29  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126  Quote:
.1234......... That's the 1:1 association. Whether or not you want to use the terminology "infinite" or "for all n" is academic.  
February 5th, 2016, 08:23 AM  #30  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra  Quote:
Perhaps you should investigate the difference between a set being countable ("listable" is a better term) and being able to say how many elements it has. Last edited by v8archie; February 5th, 2016 at 08:25 AM.  

Tags 
counting, irrational, numbers 
Search tags for this page 
set of all terminating decimals countable?,irrational number count?,Can you count to an irrational number
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Exercises on irrational numbers  AspiringPhysicist  Abstract Algebra  1  October 12th, 2014 04:15 AM 
irrational numbers  Albert.Teng  Algebra  4  February 12th, 2014 04:55 PM 
Irrational numbers  niki500  Number Theory  5  October 7th, 2012 09:10 PM 
Problem on irrational numbers  Deb_D  Number Theory  12  February 20th, 2011 11:50 AM 
Irrational Numbers  Mighty Mouse Jr  Algebra  1  October 16th, 2010 07:46 PM 