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Defining order relation

  1. Sep 18, 2012 #1

    dpa

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    1. The problem statement, all variables and given/known data

    Q. Define an order relation
    (x,y)<(j,k) if and only if x+k<y+j


    2. Relevant equations
    x<y means x+a=y and viceversa


    3. The attempt at a solution
    I have no idea. To show it is equivalence relation, I simply show that it is reflexive, transitive and symmetric. but how do I show it is order relation?
     
  2. jcsd
  3. Sep 18, 2012 #2
    Order Relation (call it C)
    1) For every x and y, with x not equal to y, xCy or yCx
    2) xCx is never true
    3) xCy, yCz implies xCz
     
  4. Sep 18, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    With a> 0, of course.


    An order relation only has to be transitive.
     
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