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Re: [PrimeNumbers] Infinite primes-> a Turing Machine prime sieve that never stops?

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  • Jud McCranie
    ... Again, those are proofs that there are an infinite number of primes. None of us disagree with that. But you are assuming that an infinite number of
    Message 1 of 21 , Nov 4 10:31 AM
      At 11:24 AM 11/4/2003, Roger Bagula wrote:
      >Other proofs at:
      ><http://www.utm.edu/research/primes/notes/proofs/infinite/index.html>http://www.utm.edu/research/primes/notes/proofs/infinite/index.html
      >
      > *
      > <http://www.utm.edu/research/primes/notes/proofs/infinite/topproof.html>Furstenberg's
      > Topological Proof (1955)
      >
      ><http://www.utm.edu/research/primes/notes/proofs/infinite/topproof.html>http://www.utm.edu/research/primes/notes/proofs/infinite/topproof.html
      >
      > *
      > <http://www.utm.edu/research/primes/notes/proofs/infinite/goldbach.html>Goldbach's
      > Proof (1730)
      >
      ><http://www.utm.edu/research/primes/notes/proofs/infinite/goldbach.html>http://www.utm.edu/research/primes/notes/proofs/infinite/goldbach.html

      Again, those are proofs that there are an infinite number of primes. None
      of us disagree with that. But you are assuming that an infinite number of
      primes implies an "infinite prime", and your own recent message says that
      isn't the case


      "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. "




      [Non-text portions of this message have been removed]
    • Paul Leyland
      Roger Bagula wrote: [Philosophical meandering deleted.] ... No, it does not. Please post again, including my text and at the appropriate point intersperse
      Message 2 of 21 , Nov 5 1:15 AM
        Roger Bagula wrote:

        [Philosophical meandering deleted.]

        > I don't know if any of this answers you list of questions or not.

        No, it does not. Please post again, including my text and at
        the appropriate point intersperse your answer to each specific
        question that I asked.

        > I really don't like to get in such discussions,

        That is becoming ever more clear as time goes by.

        > since math people seem to ignore any philosophical issues by
        > defining them away. Axioms and definitions are an answer
        > to all their thinking problems?

        Close, but no cigar. Axioms and definitions are the foundations
        of mathematical thinking. Rigorously correct logical arguments
        are the building blocks placed on the foundations. If you wish to
        be considered to be doing mathematics, please use clear and precise
        logic.

        > As a physical scientist ( chemist, physical scientist)
        > I'm not bound by those rules in my thinking.

        Ah, so you're not a mathematician and you are not interested in
        participating in mathematics. Why, then, are you making so much
        noise in an indubitably mathematical forum?

        FWIW, my background is in the physical sciences. I have a BA in
        chemistry from Oxford and my DPhil was for research in molecular
        spectroscopy. I personally don't regard that as an obstacle to
        contributing in a small way to a mathematical subject. I'm not
        bound by the rules of mathematics any more than you are, but I
        choose to follow them when communicating with mathematicians. If
        you wish to converse with practitioners of other fields of study,
        please do so but, please, do it in a relevant forum elsewhere and
        use their rules to do so. Again, FWIW, I'm quite happy to talk
        about quantum field theory or geometrodynamics, but not here.

        > In other words is science more fundamental
        > philosophically than mathematics at a metamathematical level?

        A very good question and one well worth discussing, but not here.
        It is not (IMO, the moderators may disagree) relevant to the
        advertised aims of the forum.


        Paul
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