Results 1 to 5 of 5

Math Help - Equivalence Class HELP!

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    5

    Equivalence Class HELP!

    All right I REALLY need help. I've asked a bunch of people and just don't get it.

    I understand equivalence relations. They seem easy enough, I can deal with them.

    But here's a problem I really need help with:

    a,b elements_of Z

    aRb IFF a%n = b%n = 0

    How do i get an equivalence class for this, I'm in desperate need of help!

    Thank you.

    and PS I've worked out a few pages of attempts, and the mostly end up with a = a
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,386
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by kodai View Post
    All right I REALLY need help. I've asked a bunch of people and just don't get it.

    I understand equivalence relations. They seem easy enough, I can deal with them.

    But here's a problem I really need help with:

    a,b elements_of Z

    aRb IFF a%n = b%n = 0

    How do i get an equivalence class for this, I'm in desperate need of help!

    Thank you.

    and PS I've worked out a few pages of attempts, and the mostly end up with a = a
    Here is some bad news for you.
    Your question is unreadable.
    What in the world does "aRb IFF a%n = b%n = 0" mean?
    Surely you are not asking us to 'mind read'.
    Please repost the question using standard mathematical symbols.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    5
    so sorry! I guess our teacher uses some strange notation.

    Ok a and b are elements of Z (the integers, +-)


    n is a integer
    aRb = a Related b iff (a mod n = 0 = b mod n)

    it's an equivalence relation.

    how do i go about creating an equivalence class for this relation?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Equivalence Classes

    Hello kodai
    Quote Originally Posted by kodai View Post
    so sorry! I guess our teacher uses some strange notation.

    Ok a and b are elements of Z (the integers, +-)


    n is a integer
    aRb = a Related b iff (a mod n = 0 = b mod n)

    it's an equivalence relation.

    how do i go about creating an equivalence class for this relation?
    I'm not sure that I understand the question.

    (a \mod n = 0 = b \mod n) means that a and b are both divisible by n. But it's not clear how n is defined. After all, a \mod 1 =0 for all a, so n=1 \Rightarrow \forall a, b, aRb. So we need to know something else about n.

    In the meantime, you might find the following post helpful if you want a couple of illustrations of equivalence classes: http://www.mathhelpforum.com/math-he...relations.html.

    Grandad

    PS In fact, unless n=1 it is not an equivalence relation, because (aRa \Rightarrow a \mod n = 0) \Rightarrow n|a, \forall a \in \mathbb{Z}; in other words n is a factor of every integer, which is nonsense.
    Last edited by Grandad; March 19th 2009 at 03:21 AM. Reason: Add PS
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2008
    Posts
    5
    Thank you granddad, that post REALLY cleared things up!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equivalence class
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: March 10th 2010, 09:31 AM
  2. Equivalence relation and order of each equivalence class
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2009, 09:03 AM
  3. equivalence class ?
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: October 29th 2008, 08:42 AM
  4. equivalence class
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 20th 2008, 06:32 PM
  5. Equivalence class
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: August 10th 2007, 02:50 AM

Search Tags


/mathhelpforum @mathhelpforum