February 25th, 2016, 03:41 PM  #1 
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  Prime numbers and irrational numbers
The relation between prime numbers and irrational numbers are discussed using prime line and preirrationality. A rational number is the quotient of 2 whole numbers i and j, coordinates of a points (j, i) in the plane of 2 dimensional natural numbers shown in Figure 1. Each points (j, i) represents a rational number whose value is i/j that equals the slope of the straight line connecting the point (j,i) to the origin (0,0). Please read the article at PDF Prime numbers and irrational numbers PengKuan on Maths: Prime numbers and irrational numbers or Word https://www.academia.edu/22457358/Pr...tional_numbers 
February 25th, 2016, 06:43 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
"It is not hard to imagine a infinitely big prime $P_\infty$ to be the denominator of $\dfrac{i_P}{P_\infty}$. $P_\infty$ exists because there are infinitely many primes." Actually, it is extremely difficult to imagine an infinitely big prime. What does that even mean? And no, $P_\infty$ does not exist. The reason you gave is also completely inadequate. 
February 27th, 2016, 10:36 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
It's amazing how much a person can write on a subject he knows nothing about!
Last edited by skipjack; February 27th, 2016 at 12:59 PM. 
February 27th, 2016, 10:40 AM  #4  
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  Quote:
 
February 27th, 2016, 01:17 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,655 Thanks: 2087 
The reason "because there are infinitely many primes" is inadequate.

February 27th, 2016, 01:24 PM  #6  
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  Quote:
"There are infinitely many primes, as demonstrated by Euclid around 300 BC." https://en.wikipedia.org/wiki/Prime_number  
February 27th, 2016, 03:09 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,655 Thanks: 2087 
There are infinitely many primes, but that doesn't mean that there's any "infinitely big prime". You asserted that it's not hard to imagine such a prime, then you asserted that such a prime exists.

February 27th, 2016, 05:04 PM  #8 
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  I see. Cantor asserted that aleph 0 existed. So, there is a prime that is smaller than it.

February 27th, 2016, 06:29 PM  #9 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Yes. In fact, all primes are smaller than $\aleph_0$ because they are all finite. By the way, this is very similar to the string of posts by zylo. 
February 28th, 2016, 02:30 PM  #10  
Senior Member Joined: Dec 2015 From: France Posts: 103 Thanks: 1  Quote:
Infinitely many prime numbers and infinitely many natural numbers make infinitely big prime and infinitely big natural number to exist. Infinitely big prime has the same right of existence than infinitely big number of digits.  

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irrational, numbers, prime 
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