|
|
|
|
|
|
|
|
|
 Posted: Fri Aug 04, 2006 7:41 pm
Perfect numbers are numbers whose aliquot parts add up to themselves. The aliquot parts of a number, in case you were wondering, are all of the proper divisors of that number excluding itself. So take 6 for example with aliquot parts 1, 2, and 3 1+2+3=6 so 6 is a perfect number. We know only a very few perfect numbers most of them thanks to GIMPS. One thing we do know about them is that if they are even then they are always of the form ((2^p)-1)*(2^(p-1)) where p is a prime. Take 6 for example that would be 2^(2-1)*(2^2)-1=2*3=6. We actually know relatively little else about perfect numbers though for instance we do not know if there are infinitely many of them. But more interesting to me is the fact that we still have no proof that there are no odd perfect numbers. We suspect that there aren't any of them and we have checked all the numbers up to 10^500 now but we still don't have a proof. Please just post anything you find interesting that is related to perfect numbers odd or otherwise.
|
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Tue Aug 15, 2006 11:59 am
If numbers are infinite there can be no pattern of finite.
Take the primes for example, 1,2,3,5,7,11,13,17,23...
the space between them gets bigger each time, there are more numbers between each one. But, because numbers are infinite that means there can be infinite numbers between each prime. If numbers are infinite the primes are to. That would mean that the perfects are infinite as well.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Tue Aug 15, 2006 6:32 pm
Ghama55 If numbers are infinite there can be no pattern of finite. Take the primes for example, 1,2,3,5,7,11,13,17,23... the space between them gets bigger each time, there are more numbers between each one. But, because numbers are infinite that means there can be infinite numbers between each prime. If numbers are infinite the primes are to. That would mean that the perfects are infinite as well. Unfortunately that doesn't quite work. There aren't an infinite number of integers between every prime. For instance, there are 0 integers between 2 and 3 (btw, 1 isn't prime). While there are an infinite number of prime integers, that doesn't mean that there are an infinite number of perfect integers. For instance, there is a very finite set of numbers that are equal to 5, despite there being an infinite number of integers.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Wed Aug 16, 2006 9:22 pm
thats because you are working with a finite list. You aren't trying to get all numbers, just 5. that means there will also be finite possibilities of numbers that will work out to 5. Therefore, The possibility that perfect numbers are infinite, because numbers are infinite. Imagine a circle. put a tick on the circle, now another one, only farther apart. Continue this way, each tick getting furtherfrom the last. If you can continue putting ticks in forever, there will be infinite ticks, no matter how far apart they get from the last, because the nature of a circle is infinity.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Wed Aug 16, 2006 10:15 pm
Ghama55 thats because you are working with a finite list. You aren't trying to get all numbers, just 5. that means there will also be finite possibilities of numbers that will work out to 5. If you consider the entire infinity of numbers, only finitely many will be equal to 5. The principle is the same as your reasoning; Layra-chan simply replaced the property "is an odd perfect number" with "is equal to 5." Ghama55 Therefore, The possibility that perfect numbers are infinite, because numbers are infinite. What in the world does the infinitude of numbers have to do with the possibility of odd perfect numbers? There are infinitely many numbers, yes, but it doesn't automatically mean that there are any numbers satisfying any given property "P", whether "P" is the singular "is 5" or the indetermined "is a perfect odd number" or the contradictory "is a positive number less than zero". Ghama55 Imagine a circle. put a tick on the circle, now another one, only farther apart. Continue this way, each tick getting furtherfrom the last. If you can continue putting ticks in forever, there will be infinite ticks, no matter how far apart they get from the last, because the nature of a circle is infinity. You do not have a sufficient grasp of the concept of mathematical proof. Infinity is not some magical incantation that makes everything possible. As a side note, it is possible to get only finitely many ticks on your circle if the distance is a rational multiple of π.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Sat Aug 19, 2006 7:39 pm
Touche, I have been mathimetically out fenced! I concede superiority. Until I get the lowdown on the subject from my Dad.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Reply
