February 28th, 2016, 03:19 PM  #11 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,659 Thanks: 2635 Math Focus: Mainly analysis and algebra 
We know of the existence of infinite decimals because we can know that all finite decimals are rational. We know that repeating infinite decimals exist because we can prove that they are rational. We know that nonrepeating decimals exist because we know that there are numbers that are not rational. Infinitely many primes/rationals does not imply infinitely large primes/rationals, only arbitrarily large primes/rationals. A doesn't have to have infinitely large elements to be infinitely large. For example, the set of rationals between zero and one. 
February 28th, 2016, 03:27 PM  #12  
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  Quote:
 
February 28th, 2016, 05:16 PM  #13 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,659 Thanks: 2635 Math Focus: Mainly analysis and algebra 
Primes or rationals. The statement applies equally to primes or rationals (or natural numbers).

February 28th, 2016, 05:27 PM  #14 
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  
February 28th, 2016, 05:35 PM  #15 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  
February 28th, 2016, 05:36 PM  #16  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,801 Thanks: 636 Math Focus: Yet to find out.  Quote:
 
February 28th, 2016, 05:40 PM  #17 
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  
February 28th, 2016, 05:41 PM  #18 
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  
February 28th, 2016, 05:42 PM  #19 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  
February 28th, 2016, 05:43 PM  #20 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  

Tags 
irrational, numbers, prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
prime numbers and composite numbers  shaimaa saif  Algebra  10  November 17th, 2015 08:02 AM 
irrational numbers  Albert.Teng  Algebra  4  February 12th, 2014 04:55 PM 
The paradox between prime numbers and natural numbers.  Eureka  Number Theory  4  November 3rd, 2012 03:51 AM 
Irrational numbers  niki500  Number Theory  5  October 7th, 2012 09:10 PM 
Irrational Numbers  Mighty Mouse Jr  Algebra  1  October 16th, 2010 07:46 PM 