31 1 1.6.3 Let x ∈ R. Prove that for every n ∈ N, there is r ∈ Q such that |x − r| < . n 1.6.4 Prove that if x is a rational number and y is an irrational number, then x+ y is irrational. What can you say about xy? 1.6.5 Prove that in between two real numbers x and y with x < y, there are infnitely many rational numbers. 1.6.6 Prove that in between two real numbers x and y with x < y, there are infnitely many irrational numbers.
RkJQdWJsaXNoZXIy NTc4NTAz