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Felicis@gmail.com
science forum beginner

Joined: 19 Jul 2006
Posts: 4

Posted: Thu Jul 20, 2006 2:26 pm    Post subject: Re: My prime research.

 Quote: What I am also curious is to find ways to describe how this space gets populated. Also i am interested about finding other metrics that are easy to calculate in many dimensions. angle would be one, may not be very intersting in this case though.

I don't know- clearly a pair of numbers relatively prime would be
perpendicular, and any smaller angle would be related somehow to their
common factors...

Isn't there already a body of work on infinite dimensional spaces?
Would that be applicable here?

cheers-
Eric
Virgil
science forum Guru

Joined: 24 Mar 2005
Posts: 5536

Posted: Thu Jul 20, 2006 7:38 pm    Post subject: Re: My prime research.

Felicis@gmail.com wrote:

 Quote: Hi there- I think the poster's idea was to represent natural numbers as vectors of the radices of their prime factorisation. an Idea I've encountered before - not sure where. I recently came upon this same idea on: http://mathworld.wolfram.com/ExponentVector.html from the discussion about Dixon's factorization method. I was interested in the idea of an exponent vector as a friend had thought up the idea while we were in college and I hadn't thought it would be of any use! (Of course- he came up with it independently, and long after it had already been used... Oh well, still, it was a good excuse to call him up and chat about old times...) Anyways- perhaps that is where you saw it? cheers- Eric

Would it be proper to regard these as 'vectors', when the set of
allowable "scalars" would be only the set of natural numbers and not
even a ring, much less a field?

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