If you have a set of primes that is infinite in number,

then how can the last asymptotic element at

n*log(n)

not be infinite, if n is infinite?

And since it is an element of the set of primes,

it is an infinite prime.

So the proofs which are at least four in number

that say the primes are infinite sets are either wrong

or faulted if there is no infinite last element.

It is a logical problem:

a paradox.

My answer has been to set Infinite primes as a metamathematical concept:

a definition or axiom. You either let the axiom exist or

not by "choice". You don't get all emotionally

involved as if it threatened your existence or something.

That is a "theological" reaction

not an scientifically detached one.

Mathematics isn't about "beliefs", but about facts and

deductions. Mathematics is

a "tool" for higher understanding.

One of the better ones, but still not

the end answer to all knowledge and understanding.

Philosophy is what tries to do that.

You seem to be one of the better minds in this group:

able to stretch your understanding beyond what

you where taught in school.

Paul Leyland wrote:

>> A semantic distinction needs to be made:

>>

>>Infinitely many primes is distinct from an Infinite Prime.

>>

>>Although one seems to imply the other,

>>they really involve two separate cases.

>>

>>

>

>It does indeed. We are making progress. That is precisely

>the distinction that I've been trying so hard to make

>explicit.

>

>It is my position and, I believe, that of most mathematicians

>that the term "Infinite Prime" is meaningless.

>

>I am quite prepared to be convinced that I'm wrong (I've been

>wrong enough times in the past) but to convince me you have to

>explain very clearly what you mean by the term "Infinite Prime"

>--- so clearly that even I can understand you.

>

>

>Paul

>

>

>

--

Respectfully, Roger L. Bagula

tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :

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