Results 1 to 6 of 6

Math Help - one-to-one function

  1. #1
    Member
    Joined
    Nov 2012
    From
    israel
    Posts
    164
    Thanks
    2

    one-to-one function

    I need to prove that there exist a one-to-one function: f:A\rightarrow A\times B
    where should i start?

    thanks in advanced!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: one-to-one function

    try picking a function that maps an element a to (a,___) (i'll leave it to you to decide what might go in the blank).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2012
    From
    israel
    Posts
    164
    Thanks
    2

    Re: one-to-one function

    do i just need to provide an example of a function that goes from A\rightarrow A\times B?
    (like (a, (a, b)) or (a, (a, d))...)

    im not sure what exactly do i need to prove here...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,663
    Thanks
    1616
    Awards
    1

    Re: one-to-one function

    Quote Originally Posted by Stormey View Post
    do i just need to provide an example of a function that goes from A\rightarrow A\times B?
    (like (a, (a, b)) or (a, (a, d))...)

    im not sure what exactly do i need to prove here...

    'Fix' a b\in B. Then define f:A\to (A\times B) by a\mapsto (a,b).

    Now prove f is one-to-one.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: one-to-one function

    And note that the original claim is false when B is empty but A is not.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2012
    From
    israel
    Posts
    164
    Thanks
    2

    Re: one-to-one function

    Thanks guys.
    appreciate it!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 20
    Last Post: November 27th 2012, 05:28 AM
  2. Replies: 0
    Last Post: October 19th 2011, 04:49 AM
  3. Replies: 4
    Last Post: October 27th 2010, 05:41 AM
  4. Replies: 3
    Last Post: September 14th 2010, 02:46 PM
  5. Replies: 1
    Last Post: December 3rd 2009, 08:45 AM

Search Tags


/mathhelpforum @mathhelpforum