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Re: [PrimeNumbers] Rules make the game

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  • mikeoakes2@aol.com
    ... Unfortunately for the lemma about troll-feeding, the concept of the infinite prime is a perfectly respectable one at the highest levels of number theory
    Message 1 of 5 , Nov 4, 2003
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      In a message dated 04/11/03 20:38:07 GMT Standard Time, chasag@... writes:


      > There has been a lot of discussion about prime numbers at infinity
      > and whether they exist. If your rules allow them then they exist. As
      > an example Euclid's geometry says that parallel lines never meet.
      > Non-Euclidian projective geometry allows them to meet at a so
      > called 'ideal' point at infinity. This new rule makes a much more
      > interesting geometry. Perhaps allowing an 'ideal' prime at infinity
      > might make a more interesting prime theory. I don't know. Calling
      > the idea rubbish generated by a troll is extreme.
      >

      Unfortunately for the lemma about troll-feeding, the concept of the "infinite
      prime" is a perfectly respectable one at the highest levels of number theory
      - a region so rarefied that the air is hard to breath...

      For example, there is Schlickewei's "p-adic Subspace Theorem" at:-
      http://www.stieltjes.org/archief/rep20002001/node8.html
      which certainly strikes fear into my heart.

      Mike


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