Prove that the set of irrational numbers is uncountable. Note that we cannot use the method for proving that the set of real numbers is uncountable. Explain why? Then use another method to prove it.
a) By Cantor's Diagonal Argument
b) By Constructing a One-to-One Correspondence with the Set of Real Numbers
c) By Using the Method of Nested Intervals
d) By Indirect Proof