Results 1 to 4 of 4

Math Help - Proof...did I do it?

  1. #1
    Member
    Joined
    May 2008
    Posts
    109

    Unhappy Proof...did I do it?

    Here I go again with these proofs, this time I am trying to prove the sum of two rational numbers is rational.

    This is what I have...

    Assume x is rational
    Assume y is rational
    Let x=a/b where a and b are integers and b does not equal 0
    Let y=c/d where c and d are integers and d does not equal 0
    x+y=a/b+c/d=(ad+bc)/bd
    Let w=ad+bc
    Let v=bd
    We check that w and v are integers which they are and the integers are closed under addition and multiplication
    Therefore the sum of two rational numbers is rational
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    I'm guessing you're allowed to assume that the product of two integers is still an integer. Then you can indeed say that \frac{ad+ bc}{bd} is a rational number, i.e. the ratio of two integers.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Smile

    Quote Originally Posted by o_O View Post
    I'm guessing you're allowed to assume that the product of two integers is still an integer. Then you can indeed say that \frac{ad+ bc}{bd} is a rational number, i.e. the ratio of two integers.
    Well, he noted that \mathbb{Z} is closed under multiplication, so that seems to be the case.

    Nice work, sjenkins!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2008
    Posts
    109
    Thanks so much! Finally, I got one!!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  2. Replies: 0
    Last Post: June 29th 2010, 08:48 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum