Here's a problem I am trying to solve
Find the equivalence classes of this relation
now this is an equivalence relation. If we choose any rational number x , then we can see that
so Q itself is an equivalence class of S. Now consider irrational number like pi
if we subtract any other irrational or rational number from pi , it will not be in
(is that correct ?) So
similar conclusions can be drawn for any other irrational number. so other equivalence classes would correspond to irrational numbers where the set will
contain only that irrational number. for example , since , the base of natural logarithm is an irrational number ,
so the equivalence classes are and set corresponding to
each irrational number.
is my reasoning correct ?