February 28th, 2016, 03:19 PM  #11 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,683 Thanks: 2664 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: 7,683 Thanks: 2664 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: 1,838 Thanks: 653 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  

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irrational, numbers, prime 
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