Results 1 to 4 of 4

Math Help - Equivalence relation

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    110

    Equivalence relation

    Please could anyone confirm the following:

    This concerns the relation as defined below on the complex numbers

    z~w if Re z = Re w

    This relation is reflexive, since the Re z = Re w, so z~w.

    Let z,w be an element of a complex number, and suppose z~w. Then Re z = Re w. Hence Re w = Re z, so w~z. Thus the relation is symmetric.

    Let z,w,v be an element of a complex number, and suppose that z~w and w~v. Then Re z = Re w and Re w = Re v. It follows that Re z = re v, so z~v. Thus the relation is transitive.

    Hence this relation is an equivalence relation.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1
    Quote Originally Posted by Arron View Post
    Please could anyone confirm the following
    This concerns the relation as defined below on the complex numbers
    z~w if Re z = Re w
    Hence this relation is an equivalence relation.
    That is correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2011
    Posts
    110
    Thanks alot.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by Arron View Post
    Please could anyone confirm the following:

    This concerns the relation as defined below on the complex numbers

    z~w if Re z = Re w

    This relation is reflexive, since the Re z = Re w, so z~w.

    Let z,w be an element of a complex number, and suppose z~w. Then Re z = Re w. Hence Re w = Re z, so w~z. Thus the relation is symmetric.

    Let z,w,v be an element of a complex number, and suppose that z~w and w~v. Then Re z = Re w and Re w = Re v. It follows that Re z = re v, so z~v. Thus the relation is transitive.

    Hence this relation is an equivalence relation.

    Thanks


    Reflexivity means that z~z for all the elements z, and not what you wrote. The rest is fine.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 6th 2011, 11:46 PM
  2. equivalence relation and equivalence classes
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: January 7th 2010, 06:36 PM
  3. Equivalence relation and order of each equivalence class
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2009, 09:03 AM
  4. equivalence relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 12th 2009, 05:33 PM
  5. Equivalence relation and Equivalence classes?
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 7th 2009, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum