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February 28th, 2016, 05:45 PM   #21
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Quote:
 Originally Posted by Prakhar Number of digits.
7 and 11 are primes. They have 1 and 2 digits.

February 28th, 2016, 05:52 PM   #22
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Quote:
 Originally Posted by Pengkuan Infinitely many primes does imply infinitely large primes to exist.
You claim that the infinitude of a set of numbers implies the infinitude of at least one element in the set. Please prove that claim.

I present the set of rational numbers between zero and one. Show me the infinite member of that set, or prove that the set is not infinite.

In order to make progress, you should consider what your definition of infinite (or finite) is. The one I use in cases like this is that a number $n$ is finite if there exists a natural number $N$ greater than $n$. An infinite number is one that is not finite.

February 28th, 2016, 05:52 PM   #23
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Quote:
 Originally Posted by Pengkuan 7 and 11 are primes. They have 1 and 2 digits.
I told you to give an example of an infinitely big prime number (if you think it exists).

February 28th, 2016, 05:54 PM   #24
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Quote:
 Originally Posted by Pengkuan Prime is a natural number. As natural number can be infinite, so is prime.
There are no infinite natural numbers.

February 28th, 2016, 06:12 PM   #25
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Quote:
 Originally Posted by v8archie There are no infinite natural numbers.
So, there is not infinite prime. Only prime that increase indefinitely.

February 28th, 2016, 06:12 PM   #26
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Quote:
 Originally Posted by skipjack The reason "because there are infinitely many primes" is inadequate.
What?

February 28th, 2016, 06:13 PM   #27
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Quote:
 Originally Posted by Pengkuan Prime is a natural number. As natural number can be infinite, so is prime.
Just because the set of natural numbers is infinite, and primes exist within this set, does not mean that there exists some prime of size 'infinity'.
Im sure this is a logical fallacy of some kind.

February 28th, 2016, 06:16 PM   #28
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Quote:
 Originally Posted by Pengkuan So, there is not infinite prime. Only prime that increase indefinitely.
Natural numbers and prime numbers are infinitely many. This does not mean that a particular prime or natural number is infinitely big.

February 28th, 2016, 06:23 PM   #29
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Quote:
 Originally Posted by Pengkuan So, there is not infinite prime. Only prime that increase indefinitely.
Numbers don't increase. An infinite sequence of primes increases indefinitely, but that doesn't mean that any of them are infinitely large. They are all natural numbers after all.

February 28th, 2016, 06:25 PM   #30
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Quote:
 Originally Posted by Prakhar Natural numbers and prime numbers are infinitely many. This does not mean that a particular prime or natural number is infinitely big.
Correct.

 Tags irrational, numbers, prime

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