Introduction to Mathematical Analysis I

30 1.6 APPLICATIONS OF THE COMPLETENESS AXIOM 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 a and b with a < b , there are infinitely many rational numbers. 1.6.6 Prove that in between two real numbers a and b with a < b , there are infinitely many irrational numbers.