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Natural Numbers are positive integers, N={1,2,3,4,5,...}
A twot is a natural number which is the product of two unique primes.
For example:
6 is a twot because 2 * 3 = 6
10 is a twot because 2 * 5 = 10
14 is a twot because 2 * 7 = 14
15 is a twot because 3 * 5 = 15
Now as a twot is the product of two unique prime numbers, one of the two prime numbers must smaller than the other. Therefore we can call the smaller prime number the base prime and classify twots by their base primes
For base prime two
1st twot is 2 * 3 = 6
2nd twot is 2 * 5 = 10
3rd twot is 2 * 7 = 14
and so on
For base prime three
1st twot is 3 * 5 = 15
2nd twot is 3 * 7 = 21
3rd twot is 3 * 11 = 33
and so on
Because the number of prime numbers is infinity, we can match every twot of base prime two to a natural number. Therefore there are as many twots of base prime two as there are natural numbers.
Therefore we can say there are more twots than there are natural numbers because all the natural numbers can be matched to twots of base prime two and we still have twots of base prime three and other base primes leftover.
Yet, we know not all natural numbers are twots, in fact the set of twots is a subset of the set of Natural Numbers.
So the paradox of the twots. There are more twots than there are Natural Numbers and yet at the same time there are less twots than there are Natural Numbers.
PS: Originally, I did not call it by the name twot but by different name. Later I was told that the name I have chosen was an unmentionable word in the English language, so I had rename it to twot. 122.107.207.98 ( talk) 06:16, 13 June 2009 (UTC)
Galileo called attention to this in the 17th century and Cantor addressed many similar problems in the 19th century.
Usage note: you should say "two distinct primes" if that's what you mean. "There is a unique even prime number" means there is exactly one of those. "The prime factors of 15 are distinct; whereas those of 18 are not distinct" is the right way to use that word. Michael Hardy ( talk) 16:13, 14 June 2009 (UTC)
Can anyone prove the constant created by concatenating prime p that p+2 is also a prime
is irrational?
Assume that there are infinitely many twin primes.
Thank you for your help. Motomuku ( talk) 13:38, 13 June 2009 (UTC)
Question One: (y/y-1)^2 = 6(y/y-1)+7
Question Two:
3x(x^2 + 2x)^1/2 - 2(x^2 +2x)^3/2 = 0
Your help is much appreciated!
Thanks! —Preceding
unsigned comment added by
76.78.133.108 (
talk) 18:11, 13 June 2009 (UTC)
Mathematics desk | ||
---|---|---|
< June 12 | << May | June | Jul >> | June 14 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Natural Numbers are positive integers, N={1,2,3,4,5,...}
A twot is a natural number which is the product of two unique primes.
For example:
6 is a twot because 2 * 3 = 6
10 is a twot because 2 * 5 = 10
14 is a twot because 2 * 7 = 14
15 is a twot because 3 * 5 = 15
Now as a twot is the product of two unique prime numbers, one of the two prime numbers must smaller than the other. Therefore we can call the smaller prime number the base prime and classify twots by their base primes
For base prime two
1st twot is 2 * 3 = 6
2nd twot is 2 * 5 = 10
3rd twot is 2 * 7 = 14
and so on
For base prime three
1st twot is 3 * 5 = 15
2nd twot is 3 * 7 = 21
3rd twot is 3 * 11 = 33
and so on
Because the number of prime numbers is infinity, we can match every twot of base prime two to a natural number. Therefore there are as many twots of base prime two as there are natural numbers.
Therefore we can say there are more twots than there are natural numbers because all the natural numbers can be matched to twots of base prime two and we still have twots of base prime three and other base primes leftover.
Yet, we know not all natural numbers are twots, in fact the set of twots is a subset of the set of Natural Numbers.
So the paradox of the twots. There are more twots than there are Natural Numbers and yet at the same time there are less twots than there are Natural Numbers.
PS: Originally, I did not call it by the name twot but by different name. Later I was told that the name I have chosen was an unmentionable word in the English language, so I had rename it to twot. 122.107.207.98 ( talk) 06:16, 13 June 2009 (UTC)
Galileo called attention to this in the 17th century and Cantor addressed many similar problems in the 19th century.
Usage note: you should say "two distinct primes" if that's what you mean. "There is a unique even prime number" means there is exactly one of those. "The prime factors of 15 are distinct; whereas those of 18 are not distinct" is the right way to use that word. Michael Hardy ( talk) 16:13, 14 June 2009 (UTC)
Can anyone prove the constant created by concatenating prime p that p+2 is also a prime
is irrational?
Assume that there are infinitely many twin primes.
Thank you for your help. Motomuku ( talk) 13:38, 13 June 2009 (UTC)
Question One: (y/y-1)^2 = 6(y/y-1)+7
Question Two:
3x(x^2 + 2x)^1/2 - 2(x^2 +2x)^3/2 = 0
Your help is much appreciated!
Thanks! —Preceding
unsigned comment added by
76.78.133.108 (
talk) 18:11, 13 June 2009 (UTC)