Results 1 to 3 of 3

Math Help - Well-Ordering Proof

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    86

    Well-Ordering Proof

    Hey all, I would appreciate some help with the following proof:

    Let A be a nonempty subset of Z and b is an element of the Integers, such that for each a which is an element of A, b <= a. Then A has a smallest element.

    I think the Well-Ordering Principle is supposed to be used here..thanks for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    If b is in A, then b is the smallest element. Otherwise, b+1 is a lower bound on A, and you repeat the argument--if b+1 is in A, then b+1 is the smallest element, otherwise b+2 is a lower bound on A. This won't continue forever, because A is nonempty. Pick any a in A, and this process will terminate in no more than b-a steps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    86
    Hmm how would I go about writing this in a proof?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: November 25th 2010, 12:11 PM
  2. Ordering proof?
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: June 25th 2010, 03:10 AM
  3. Proof using Well Ordering
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 27th 2010, 11:17 PM
  4. Well Ordering Proof?
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: January 14th 2010, 07:31 PM
  5. Well-Ordering Proof Skeleton
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: January 31st 2009, 11:31 AM

Search Tags


/mathhelpforum @mathhelpforum