In mathematics, nearly all significant irrational numbers can be expressed as a sum of an infinite convergent series, but according to law of addition of rational numbers, adding any to rational numbers can not result in an irrational number.
So, why is this contradiction?
Adding any two rational numbers results in a rational number. By induction, adding any finite number of rational numbers together results in a rational number.
Adding together infinitely many rational numbers has no such guarantee, in exactly the same way that there is no guarantee that such a sum is finite.