Just to clarify because we know the defintion of ratinal num

Just to clarify, because we know the defintion of ratinal numbers is the set of all ordered pairs of the same equivalence class. Thus [(x,y)] means x/y and we have to prove why x/y=1 if x=y.

Let x E Z and y e Z*. Prove that [(x,)] = 1 if and only if x =y. Just to clarify, because we know the defintion of ratinal numbers is the set of all ordered pairs of the same equivalence class. Thus [(x,y)] means x/y and we have to prove why x/y=1 if x=y.

Solution

TO PROVE - : [(x,y)] if x=y.

[(x,y)] = x / y                  (According to the question)

case :- when x = y   and   x and y not equal to 0

=> [(x,y)] = x / y = x / x = 1                 (since , x and y are equal)

hence , [(x,y)] = 1 only when x = y and they are equal to 0

hence proved :)