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 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 pre-irrationality. 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
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Quote:
 Originally Posted by Azzajazz "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.
What reason is completely inadequate?

 February 27th, 2016, 01:17 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 The reason "because there are infinitely many primes" is inadequate.
February 27th, 2016, 01:24 PM   #6
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 Originally Posted by skipjack The reason "because there are infinitely many primes" is inadequate.
Is the following incorrect?
"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: 20,972 Thanks: 2222 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
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 Originally Posted by skipjack 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.
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
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 Originally Posted by Azzajazz 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.
In fact, infinitely big prime has the same function than infinitely many digits. When people talk about irrational numbers, they say that the number of digits is infinite. This idea is well accepted, but who has seen an infinitely big number?

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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