Results 1 to 4 of 4

Math Help - real analysis

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    172

    real analysis

    prove that for each  x \in \mathbb{ R}  \mbox { and each} \    n \in \mathbb{ N }
     \mbox { there is rational number} \\   \mbox {rn   such that }  \    \mid r n    - x \mid< \frac{1}{n}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,824
    Thanks
    1717
    Awards
    1
    Quote Originally Posted by flower3 View Post
    prove that for each  x \in \mathbb{ R}  \mbox { and each} \    n \in \mathbb{ N }
     \mbox { there is rational number} \\   \mbox {rn   such that }  \    \mid r n    - x \mid< \frac{1}{n}
    Is there a rational number between these two numbers \frac{x}<br />
{n} - \frac{1}<br />
{{n^2 }}\;\& \,\frac{x}<br />
{n} + \frac{1}<br />
{{n^2 }}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    172
    Is there a rational number between these two numbers sure!!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,824
    Thanks
    1717
    Awards
    1
    Quote Originally Posted by flower3 View Post
    Is there a rational number between these two numbers sure!!!
    Well call it r.
    Then you are done if you multiply by n and write the interval in absolute value form.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Real analysis
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 1st 2010, 04:37 AM
  2. Real analysis help please
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 19th 2009, 05:31 PM
  3. real analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 19th 2009, 12:44 PM
  4. real analysis
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: August 18th 2009, 12:32 AM
  5. Real Analysis
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 12th 2008, 05:34 PM

Search Tags


/mathhelpforum @mathhelpforum