Is (x,y)<(j,k) Defined as an Order Relation by x+k<y+j?

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SUMMARY

The discussion centers on defining the order relation (x,y) < (j,k) based on the condition x + k < y + j. Participants explore the properties required for this relation to qualify as an order relation, specifically focusing on transitivity, reflexivity, and symmetry. It is established that for a relation to be an order relation, it must be transitive, and the reflexive property does not hold true in this case. The conclusion emphasizes that the relation is indeed an order relation due to its transitive nature.

PREREQUISITES
  • Understanding of order relations in mathematics
  • Familiarity with reflexive, transitive, and symmetric properties
  • Basic knowledge of inequalities and their implications
  • Concept of equivalence relations
NEXT STEPS
  • Study the properties of order relations in detail
  • Learn about equivalence relations and their distinctions from order relations
  • Explore examples of transitive relations in mathematical contexts
  • Investigate the implications of inequalities in defining relations
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Mathematics students, educators, and anyone interested in the foundational concepts of order and equivalence relations in set theory.

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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?
 
Physics news on Phys.org
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
 
dpa said:

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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