Results 1 to 2 of 2

Thread: Well-defined map

  1. February 18th 2009, 06:38 AM #1
    peteryellow
    peteryellow is offline
    Member
    Joined
    Aug 2008
    Posts
    97

    Well-defined map

    How can I show that the map, here Z= integers

    \phi: Z/3Z /times Z/3Z ---> Z/3Z defined by phi(x,y) = xy is well-defined.
    Follow Math Help Forum on Facebook and Google+
  2. February 18th 2009, 05:46 PM #2
    ThePerfectHacker
    ThePerfectHacker is offline
    Global Moderator ThePerfectHacker's Avatar
    Joined
    Nov 2005
    From
    New York City
    Posts
    10,603
    Quote Originally Posted by peteryellow View Post
    How can I show that the map, here Z= integers

    \phi: Z/3Z /times Z/3Z ---> Z/3Z defined by phi(x,y) = xy is well-defined.
    If [x_1]=[x_2] and [y_1]=[y_2] then it means x_1\equiv x_2(\bmod 3) and y_1\equiv y_2(\bmod 3).
    Therefore, x_1y_1\equiv x_2y_2(\bmod 3) and so [x_1y_1] = [x_2y_2].
    Follow Math Help Forum on Facebook and Google+
« Difference between base and ordered base | residually finite groups »

Similar Math Help Forum Discussions

  1. f(t) = t^2 defined for 0 < t <= 2 pi. Even or not?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 17th 2011, 01:46 AM
  2. Which of the following is not defined?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 12th 2009, 02:23 PM
  3. Well defined
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: September 22nd 2009, 11:03 PM
  4. In Matlab, how to refer a self-defined function in another self-defined function?
    Posted in the Math Software Forum
    Replies: 2
    Last Post: August 5th 2009, 10:20 AM
  5. well defined
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 22nd 2008, 01:06 PM

Search Tags


/mathhelpforum @mathhelpforum