Results 1 to 2 of 2

Math Help - Proof utilizing archemedian principle

  1. #1
    Senior Member Pinkk's Avatar
    Joined
    Mar 2009
    From
    Uptown Manhattan, NY, USA
    Posts
    419

    Proof utilizing archemedian principle

    Prove that if a > 0, then there exists  n \in \mathbb{N} such that  \frac{1}{n} < a < n

    I know the Archemedian Principle comes into play, but I'm just having a brain freeze on how to do this.

    EDIT: Bleh, nevermind. I figured it out.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Pinkk View Post
    Prove that if a > 0, then there exists  n \in \mathbb{N} such that  \frac{1}{n} < a < n

    I know the Archemedian Principle comes into play, but I'm just having a brain freeze on how to do this.

    EDIT: Bleh, nevermind. I figured it out.
    By the archimedean principle there exists an n\in\mathbb{N} such that \frac{1}{n}<a. Take n'=\max\left\{a,n+1\right\}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inclusion-Exclusion Principle Proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 27th 2011, 09:50 AM
  2. Problem utilizing order statistics
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 25th 2011, 06:59 PM
  3. A word problem utilizing matrices.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 15th 2010, 12:03 AM
  4. Non-Trivial Proof Using Pigeonhole Principle
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 17th 2008, 11:26 PM
  5. Principle of Induction Proof
    Posted in the Algebra Forum
    Replies: 9
    Last Post: October 14th 2008, 10:57 AM

Search Tags


/mathhelpforum @mathhelpforum