Results 1 to 5 of 5

Math Help - Bijection and Functions

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    44

    Bijection and Functions

    Hi, I need some help with understanding bijective functions.

    Is the function f(a,b) = (a+1,b) for all (a,b) bijective? I think not because x is not equal to y. Can some please help me with this?

    Also similar to this,

    f(a,b) = a-1 for all (a,b). Is this function onto or bijective?


    Thnaks alot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by kurac View Post
    Hi, I need some help with understanding bijective functions.

    Is the function f(a,b) = (a+1,b) for all (a,b) bijective? I think not because x is not equal to y. Can some please help me with this?

    Also similar to this,

    f(a,b) = a-1 for all (a,b). Is this function onto or bijective?


    Thnaks alot.
    please state the domain and ranges for the functions you have. where are a and b from, where are x and y from?

    a function is bijective if it is both one to one and onto, so just check those properties. without more info, can't help you beyond that.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    Thanks for replying.

    Well, lets just consider Z^2, the set of all pairs (a,b), where a, b elements (E) of Z. (Z is domain, collection of all integers)

    Hope that is clearer, its all i have been supplied with in my textbook.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2009
    Posts
    44
    ignore x and y, i meant to refer to a and b. I dont want to confuse anyone or myself know, im confused enough
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Bijection

    Hello kurac
    Quote Originally Posted by kurac View Post
    Is the function f(a,b) = (a+1,b) for all (a,b) bijective?
    Yes, if the domain is the whole of \mathbb{Z}^2. You can think of \mathbb{Z}^2 as a lattice of points in the (x, y) plane with integer coordinates. The function f(a, b) = (a+1, b), then, maps a point onto its immediate neighbour 1 unit to the right. So it's both one-to-one and onto.

    f(a,b) = a-1 for all (a,b). Is this function onto or bijective?
    Presumably, this function is from \mathbb{Z}^2 to \mathbb{Z}?

    If so, it will certainly be onto, because \forall n \in \mathbb{Z}, \exists a \in \mathbb{Z}, a-1=n.

    But it's not one-to-one, because for a given value of a, there are infinitely many possible values of b for which f(a,b) = a-1. So it is not bijective.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] bijection between two sets of functions
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: January 2nd 2012, 02:18 AM
  2. Bijection
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 7th 2010, 07:24 AM
  3. Bijection
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 11th 2009, 05:28 AM
  4. Bijection functions and inverses
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 29th 2009, 10:28 AM
  5. Bijection
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2006, 03:42 PM

Search Tags


/mathhelpforum @mathhelpforum