Results 1 to 4 of 4

Math Help - Help with a proof please!

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    14

    Help with a proof please!

    I need help with this question. It says to use Corollary 5.10(meaning this: A finite set is not equivalent to any of its proper subsets) to show that the rationals Q are infinite.

    How would I go about doing this?

    Thanks for your help!
    Last edited by calcprincess88; April 25th 2008 at 08:21 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by calcprincess88 View Post
    I need help with this question. It says to use Corollary 5.10(meaning this: A finite set is not equivalent to any of its proper subsets) to show that the rationals Q are infinite.

    How would I go about doing this?

    Thanks for your help!
    Lets rewrite the Corollary as an if then statement

    If a Set is finite then it is not equivelent to any of its proper subsets
    p \implies q

    Use the contrapositive of this corollary.
    \sim q \implies \sim p

    if a set is equivelent to any of its proper subsets, then the set is infinite

    See what you can do from here.

    Good luck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    If a set is equivelent to any of its proper subsets, then the set is infinite
    Hint: Show that \mathbb{Z} is equivalent to \mathbb{Q}. Use the Cantors famous diagonal trick. See Proof that rational numbers are countable - from Homeschool Math
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2008
    Posts
    14
    Thanks for your help! I'll try to do it and see what I can come up with and if I need anymore help I'll come back! Thanks again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 11:50 AM
  2. Replies: 0
    Last Post: June 29th 2010, 09:48 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 11:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 02:20 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, 05:07 PM

Search Tags


/mathhelpforum @mathhelpforum