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 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 non-repeating 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
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Quote:
 Originally Posted by v8archie 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 non-repeating 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.
What is primes/rationals?

 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
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 Originally Posted by v8archie Primes or rationals. The statement applies equally to primes or rationals (or natural numbers).
Infinitely many primes does imply infinitely large primes to exist.

February 28th, 2016, 05:35 PM   #15
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 Originally Posted by Pengkuan Infinitely many primes does imply infinitely large primes to exist.
No. Length of any prime number is fixed even if it is too large. If you think so, give an example.

February 28th, 2016, 05:36 PM   #16
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 Infinitely many primes does imply infinitely large primes to exist.
Prove it

February 28th, 2016, 05:40 PM   #17
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Quote:
 Originally Posted by Prakhar No. Length of any prime number is fixed even if it is too large. If you think so, give an example.
What is length of prime number?

February 28th, 2016, 05:41 PM   #18
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Quote:
 Originally Posted by Joppy Prove it
Prime is a natural number. As natural number can be infinite, so is prime.

February 28th, 2016, 05:42 PM   #19
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Quote:
 Originally Posted by Pengkuan What is length of prime number?
Number of digits.

February 28th, 2016, 05:43 PM   #20
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 Originally Posted by Pengkuan Prime is a natural number. As natural number can be infinite, so is prime.
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