Results 1 to 4 of 4

Math Help - Help with a Proof

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    8

    Help with a Proof

    The set of all integers (positive , Negative, and 0 ) is denumerable?

    How do you prove this? I have

    Set Z = (....-3, -2, -1, 0 , 1 , 2 , 3 ....)

    Proof : Z = ( 0, 1, -1, 2, -2, 3, -3...) is this right??


    Thank you so much!
    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 mattman3377 View Post
    The set of all integers (positive , Negative, and 0 ) is denumerable?

    How do you prove this? I have

    Set Z = (....-3, -2, -1, 0 , 1 , 2 , 3 ....)

    Proof : Z = ( 0, 1, -1, 2, -2, 3, -3...) is this right??


    Thank you so much!
    Not quite you need to define a bijection (1-1 and onto) function from
    \mathbb{Z} \to \mathbb{N}

    Hint: use a piecewise and send the non positive integers (0,-1,-2,...) to the odd natural numbers and send the positive integers to the even natural numbers.

    Good luck
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    8
    First, Thank you so much for your speedy response!

    I have a test tomorrow and this is all the teacher gave us to study for ( what I wrote to you)

    I'm not quite sure what a bijection means?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by mattman3377 View Post
    First, Thank you so much for your speedy response!

    I have a test tomorrow and this is all the teacher gave us to study for ( what I wrote to you)

    I'm not quite sure what a bijection means?
    bijection is a function that is both 1-1 and onto
    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