Results 1 to 2 of 2

Math Help - equivalence relation

  1. #1
    Banned
    Joined
    Mar 2011
    Posts
    118

    equivalence relation

    Let R be the relation on N such that aRb when a/b is an integer power of 2. Show the least element of an equivalance class is odd.

    Ok so I get its always a prime but how do I prove it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    Let n be the smallest representative of [n] (a smallest element exists by well-ordering). If n is even, then n=2m for some m<n, and then mRn, contradicting that n was the smallest representative of the class.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 7th 2011, 12:46 AM
  2. equivalence relation and equivalence classes
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: January 7th 2010, 07:36 PM
  3. Equivalence relation and order of each equivalence class
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2009, 10:03 AM
  4. equivalence relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 12th 2009, 06:33 PM
  5. Equivalence relation and Equivalence classes?
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 7th 2009, 04:39 AM

Search Tags


/mathhelpforum @mathhelpforum