Infinity Is a Prime Number - Care to Discuss?
The other day I was discussing with a fellow mathematician
whether or not infinity was a prime number, and we were also discussing
the Fibonacci sequences. In the Fibonacci sequences as you get higher in
numbers, the spaces between the Fibonacci numbers become farther and
further apart. So if you were to get to infinity, and granted you could
never get there, but if you could you'd realize that it isn't divisible
by anything. How far back would you have to go to find a Fibonacci
number?
This turns out to be a very interesting question, and answer would be; quite a long way, but we can't know the answer. Is there a point at which we could know the answer? Some mathematicians would submit that there is, but I'd hold my opinion until I saw the proof.
Is infinity a prime number?
This was another question we asked ourselves, and remember much of this is philosophy and not only mathematics. So let's look at the definition of a prime number;
"A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a compound number. For example, 5 is prime because only 1 and 5 divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6,"
Source: WikiPedia.
If we look at this strict definition, one could say that infinity can only be a prime number. However let's say in the case of the concept of the universe as "ever expanding" that as it expands it would be a prime more often, but not always. Does that make sense? If you knew the speed at which your set consisting of infinity was expanding, you could determine what percentage of the time infinity was a prime, because you know the rate of change.
Still, the only time it might not be a prime number would be "in the past" at a point in which you had measured it, that point in time and that number of course no longer exist even as you are rapidly calculating the answer, you see that point? If you can know one of these past so-called points in time, then we can write a proof showing that perhaps at that point infinity was or wasn't a prime number, but if you can prove it wasn't there is a good chance it was.
Now then, we also often subtract sets from infinity, and measure the rate of change of those sets, it stands to reason that we can come to some sort of probability and proximity of when the infinity is a prime, and how often it changes from a prime to a non-prime number based on this logic.
There is another counter argument that says that infinity can never be a prime number because infinity can never be known, and infinity cannot be static measurement, because it would be all that is, thus it could not be infinity. Still, if infinity is all there is, it could also be known as "one" with everything, and of course we know that one is indeed a prime.
If infinity is larger than any number you can come up with, then how can you divide it by any other number, because it would always be larger than whatever you came up with after working your equation.
Nevertheless, it stands to reason that infinity has to be a prime, and that it cannot be anything else. This completely throws a loop in what humans are often taught when considering the concept of infinity, even though it is a leap of faith to mentally understand the full extent of the concept. Indeed, I hope you too have enjoyed a little extra mathematical and philosophical stimulus today. Please consider all this and think on it.
This turns out to be a very interesting question, and answer would be; quite a long way, but we can't know the answer. Is there a point at which we could know the answer? Some mathematicians would submit that there is, but I'd hold my opinion until I saw the proof.
Is infinity a prime number?
This was another question we asked ourselves, and remember much of this is philosophy and not only mathematics. So let's look at the definition of a prime number;
"A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a compound number. For example, 5 is prime because only 1 and 5 divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6,"
Source: WikiPedia.
If we look at this strict definition, one could say that infinity can only be a prime number. However let's say in the case of the concept of the universe as "ever expanding" that as it expands it would be a prime more often, but not always. Does that make sense? If you knew the speed at which your set consisting of infinity was expanding, you could determine what percentage of the time infinity was a prime, because you know the rate of change.
Still, the only time it might not be a prime number would be "in the past" at a point in which you had measured it, that point in time and that number of course no longer exist even as you are rapidly calculating the answer, you see that point? If you can know one of these past so-called points in time, then we can write a proof showing that perhaps at that point infinity was or wasn't a prime number, but if you can prove it wasn't there is a good chance it was.
Now then, we also often subtract sets from infinity, and measure the rate of change of those sets, it stands to reason that we can come to some sort of probability and proximity of when the infinity is a prime, and how often it changes from a prime to a non-prime number based on this logic.
There is another counter argument that says that infinity can never be a prime number because infinity can never be known, and infinity cannot be static measurement, because it would be all that is, thus it could not be infinity. Still, if infinity is all there is, it could also be known as "one" with everything, and of course we know that one is indeed a prime.
If infinity is larger than any number you can come up with, then how can you divide it by any other number, because it would always be larger than whatever you came up with after working your equation.
Nevertheless, it stands to reason that infinity has to be a prime, and that it cannot be anything else. This completely throws a loop in what humans are often taught when considering the concept of infinity, even though it is a leap of faith to mentally understand the full extent of the concept. Indeed, I hope you too have enjoyed a little extra mathematical and philosophical stimulus today. Please consider all this and think on it.
Lance Winslow has launched a new provocative series of eBooks on the Future of Education. Lance Winslow is a retired Founder of a Nationwide Franchise Chain, and now runs the Online Think Tank; http://www.worldthinktank.net
Article Source:
http://EzineArticles.com/?expert=Lance_Winslow
Aucun commentaire:
Enregistrer un commentaire