Results 1 to 2 of 2

Math Help - Bijection

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    23

    Bijection

    Let f: Z_5--->Z_5 be the function defined by f([a])=[2a+3]. Show that f is well-defined, and determine whether f is bijective.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2008
    From
    Westwood, Los Angeles, CA
    Posts
    176
    Thanks
    1
    So your function looks like:

    f(0) = 3
    f(1) = 5 = 0
    f(2) = 7 = 2
    f(3) = 9 = 4
    f(4) = 11 = 1.

    In order for it to be well-defined, when we put each input, we should get exactly one output (i.e., f(a) can't be equal to two different things for a given a). Looks like our function is well-defined - when we put each thing in, we get out exactly one thing.

    In order to be bijective, it has to be one-to-one and onto.

    One-to-one means that each thing in the range has no more than one thing that maps to it. Clearly, this is true from the above table.

    Onto means that everything in the range (Z_5) gets mapped to. Z_5 consists of 0, 1, 2, 3, and 4, and they all get mapped to by something.

    So it looks both one-to-one and onto, and thus bijective.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bijection
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 6th 2010, 12:58 AM
  2. Bijection
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 10:14 AM
  3. bijection of e^x * ln x
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 20th 2010, 12:46 PM
  4. bijection help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 12th 2009, 07:59 PM
  5. Bijection
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2006, 02:42 PM

Search Tags


/mathhelpforum @mathhelpforum