Results 1 to 4 of 4

Math Help - Floor Function

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Floor Function

    Prove:
    \displaystyle\left \lfloor \frac{n}{2} \right \rfloor=\frac{n-1}{2} \ \mbox{if n is odd}

    Since n is odd, \displaystyle n=2p+1 \ \ni \ p\in\mathbb{Z}

    \displaystyle\left \lfloor \frac{2p+1}{2} \right \rfloor but I am not sure how that will help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    As a hint, consider \frac{2p+1}{2}=p+\frac{1}{2}. Then, \lfloor p+\frac{1}{2}\rfloor=p.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    I have that down as well but don't see the connection.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    Then what is \frac{n-1}{2}?

    It is \frac{n-1}{2}=\frac{(2p+1)-1}{2}=\frac{2p}{2}=p.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit of a floor function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 4th 2011, 09:58 AM
  2. Help with floor function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2010, 12:51 PM
  3. Replies: 1
    Last Post: December 3rd 2009, 09:45 AM
  4. Floor function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: June 23rd 2009, 11:03 PM
  5. Floor function
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: December 21st 2008, 11:13 PM

/mathhelpforum @mathhelpforum