Results 1 to 2 of 2

Math Help - finite sets

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    53

    finite sets

    Prove that every finite set has measure zero.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by friday616 View Post
    Prove that every finite set has measure zero.
    Let X be a finite set X=\{x_1, x_2, ..., x_n\}.

    Let \epsilon >0 and choose a cover for X,
    \{(x_i - \frac{\epsilon}{3n}, x_i + \frac{\epsilon}{3n})\}_{i=1}^n

    Then \sum_{i=1}^{n}[(x_i + \frac{\epsilon}{3n})- (x_i - \frac{\epsilon}{3n})] = n \frac{2 \epsilon}{3n}= \frac{2\epsilon}{3} < \epsilon

    Thus X is of measure zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finite and infinite sets
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: August 6th 2011, 03:53 PM
  2. Finite SETS
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 8th 2010, 07:04 AM
  3. question on finite sets
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 20th 2009, 09:03 AM
  4. Proof: finite sets
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 26th 2009, 10:01 PM
  5. Need help...recursion/finite sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 14th 2006, 08:32 PM

Search Tags


/mathhelpforum @mathhelpforum