Every perfect set is not discrete?? Let X be a set with discrete topology. So, every singletons are open. This means every point in X can not be a limit point of X. If X is perfect, every point must be limit point, but it is not. Thus, perfect set can’t be discrete. 
I wanted to show that Cantor set is not discrete, and therefore infinite product of {0,1} with discrete topology is not discrete since it is homeomorphic to Cantor set.
Am I right??

Yes, it is correct. Personally, I think that proving that the Cantor set is not discrete directly from the definition (of the Cantor set) is more natural, but it's a matter of taste.
