Results 1 to 6 of 6

Math Help - Order Relation

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    Germany
    Posts
    5

    Order Relation

    Q. Define an order relation

    (x,y)<(j,k) if and only if x+k<y+j

    I do not any idea where to start?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Order Relation

    Quote Originally Posted by keynes View Post
    Q. Define an order relation
    (x,y)<(j,k) if and only if x+k<y+j I do not any idea where to start?
    BUT what is the question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    Germany
    Posts
    5

    Re: Order Relation

    The whole question is:

    We defined Z to be the set of equivalence classes of tuples (x,y) with a,b is in Z with respect to the equivalence relation
    (x,y)~(x',y') if and only if x+y'=x'+y
    Define an order relation by
    (x,y)<(j,k) if and only if x+k<y+j
    Show that if (x,y)~(x',y') and (x,y)<(j,k) then (x',y')<(j,k). {{I can solve this part if the above part is defined}}
    Dont we have to show that the order relation is defined. Like, when asked to define a given equivalence relation, we showed that the relation is transitive, reflexive and symmetric?
    :-)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Order Relation

    Quote Originally Posted by keynes View Post
    The whole question is:
    We defined Z to be the set of equivalence classes of tuples (x,y) with a,b is in Z with respect to the equivalence relation
    (x,y)~(x',y') if and only if x+y'=x'+y
    Define an order relation by
    (x,y)<(j,k) if and only if x+k<y+j
    Show that if (x,y)~(x',y') and (x,y)<(j,k) then (x',y')<(j,k). {{I can solve this part if the above part is defined}}
    Dont we have to show that the order relation is defined. Like, when asked to define a given equivalence relation, we showed that the relation is transitive, reflexive and symmetric?
    Sorry to say that still makes no sense for me. It may be a translation problem.
    What is the 'underlying' set?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2012
    From
    Germany
    Posts
    5

    Re: Order Relation

    There is no underlying set except Z, the set of integers. if thats what you mean.
    we defined the set of integers to be the set of equivalence classes of tuples... means that's what we proved in class.
    and order relation means greater than or smaller than order, not ordered pair type order.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774

    Re: Order Relation

    When one says, "Define an order relation," it may mean "Define a relation about which we will later prove that it is an order." The phrase "Define an order relation by (x,y)<(j,k) if and only if x+k<y+j" defines a relation. First, one needs to show that < is well-defined. This means that the result of comparison does not depend on the representative of the equivalence class we use. This is exactly what the problem asks to show. Later presumably one is supposed to prove that < is an order.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 3rd Order Recurrence Relation
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 26th 2011, 03:44 AM
  2. Partial Order Relation help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 11th 2011, 12:29 AM
  3. last two problems. order relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2006, 01:30 PM
  4. Order/Relation Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2006, 09:51 AM
  5. Partial order relation
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: April 17th 2006, 01:34 PM

Search Tags


/mathhelpforum @mathhelpforum