Loading ...
Sorry, an error occurred while loading the content.

A Little Challenge

Expand Messages
  • Marty Weissman
    If I had to give my #1 reason for my interest in prime numbers, I d have to say that it goes back to my first reading Euclid s proof of their infinity. How
    Message 1 of 1 , Dec 2, 2001
    • 0 Attachment
      If I had to give my #1 reason for my interest in prime numbers, I'd have
      to say that it goes back to my first reading Euclid's proof of their
      infinity. How simple and concise a proof of such magnitude that it took
      so many, many years before it was discovered. Elegance is the word
      describing such an effort. The fact that there are so many as yet
      unsolved conjectures involving the primes is impetus to keep one's
      interest in the topic alive.

      But now to a slightly different topic: I still vividly recall a theorem
      involving the real numbers which also has an elegant and fairly short
      (but quite difficult to come up with quickly) proof. I posted this a
      while ago, but got no replies. In any case, it would be an interesting
      challenge to see if you can come up with it. If anyone wants the
      solution, just email me at mweissm2@... ---- Marty Weissman

      Statement of problem:

      Let S represent a set of real numbers (called a "POSITIVE CLASS") with
      the following
      properties: (1) For every real number x, either x belongs to S, -x
      belongs to S, or x = 0, and all
      three are mutually exclusive. (2) If x and y belong to S, then so does x

      + y and xy. Clearly, the
      set of positive real numbers form a "POSITIVE CLASS". The problem is to

      prove that this is,
      in fact, the only set of real numbers which do form a "POSITIVE CLASS".
    Your message has been successfully submitted and would be delivered to recipients shortly.