
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
January 13th, 2016, 06:12 PM  #21 
Global Moderator Joined: Dec 2006 Posts: 20,648 Thanks: 2085 
You explicitly list various finite decimals, but those are immaterial, as it's undisputed that they're countable. Their countability doesn't imply that the infinite decimals are countable. You're effectively asserting that such an implication exists, but it doesn't, and a mere assertion doesn't constitute a proof. You could provide 3, 3.1, 3.141, 3.1415, 3.14159, . . . $\pi$, and I would be happy with that. However, that way of dealing with irrational numbers uses a subset of the rationals, and there are uncountably many subsets of the rationals, so you don't have a countable number of countable numbers with that approach. 
January 13th, 2016, 06:41 PM  #22 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra  I know what an infinite decimal is. Your problem is that every $n$ is finite. You appear not to understand that the notation $\sum \limits_{n=1}^\infty a_n$ (which is what you are effectively doing: $a_n = 10^n$) includes only finite values of $n$ because there is no infinite natural number. 
February 29th, 2016, 03:19 AM  #23 
Global Moderator Joined: Dec 2006 Posts: 20,648 Thanks: 2085  
February 29th, 2016, 06:24 AM  #24 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra  
February 29th, 2016, 08:46 AM  #25 
Member Joined: Aug 2014 From: Somewhere between order and chaos Posts: 44 Thanks: 5 Math Focus: Set theory, abstract algebra, analysis, computer science  

Tags 
countable, numbers, real 
Search tags for this page 
recurring decimal are counrltable,recurring decimal number is countable?,recurring decimals are countable,terminating and non terminating decimals wikipedia
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Real numbers  Congeniality  Math Books  2  June 10th, 2015 08:25 AM 
real numbers  jessjans11  Algebra  9  July 22nd, 2014 03:20 AM 
Let a,b be real numbers such that....  thehurtlooker  Algebra  3  April 9th, 2013 12:58 AM 
Real Numbers  Tartarus  Algebra  2  November 26th, 2009 01:28 PM 
The Real Line & Countable Complement Topology not Compact?  TTB3  Topology  1  December 22nd, 2008 04:30 PM 