Assignment:
Formal Math Proofs
Prove that each of the following sets is countable:
a) The set of all numbers with two distinct decimal expansions (like 0.500... and 0.4999...);
b) The set of all rational points in the plane (i.e., points with rational coordinates);
c) The set of all rational intervals (i.e., intervals with rational end points);
d) The set of all polynomials with rational coefficients.
Provide complete and step by step solution for the question and show calculations and use formulas.