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Defining order relation

  • Thread starter dpa
  • Start date
  • #1
dpa
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Homework Statement



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


Homework Equations


x<y means x+a=y and viceversa


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?
 

Answers and Replies

  • #2
91
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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
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,772
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Homework Statement



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


Homework Equations


x<y means x+a=y and viceversa
With a> 0, of course.


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?
An order relation only has to be transitive.
 

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