I'm having trouble understanding whether or not this relation would be considered antisymmetric and transitive. The a relation R on the set of real numbers by (x,y) ϵ R if and only if x-y=0. If I am understanding this correctly the this set would be correct:
R= { (1,1) (2,2) (3,3) (4,4) (5,5) }
It is clearly reflexive but I'm having trouble understanding whether or not it is antisymmetric and transitive.