How the set of real no is uncountable?

Answer 1

There is no one to one correspondence between the real numbers and the set of integers. In fact, the cardinality of the real numbers is the same as the cardinality of the power set of the set of integers, that is, the set of all subsets of the set of integers.

Answer 2

You need to read Cantor's diagonal argument (Google it and go for the Wikipedia page). It does not require a great deal of prior knowledge to appreciate the proof.