Prove that the set S e2x x E N is denumerable What is the

Prove that the set S = {e^2x : x E N } is denumerable. What is the cardinality of S? Prove that the subset A = {x B : x is irrational} of the open interval B = (0, 1) is uncountable

Solution

B) UNION OF two countable sets is countable.

if A is countable then since C = (0,1) intersection Q is countable

A+C = B = (0,1) is countable

contradiction

a) By the definition it seems countable . clarify the definition of S

So A is not countable