TEST BANK FOR Principles of Mathematical Analysis By Walter Rudin

The Real and Complex Number Systems Unless the contrary is explicitly stated, all numbers that are mentioned in these exercises are understood to be real. 1.1 Problems on rational numbers and fields Rudin Chapter 1 Exercise 1. Problem 1.1 Proof. Assume that r + x was rational. Then it follows from Definition 1.12(A1), (A4) and (A5) that x = (r + x) − x is also rational, a contradiction. Similarly, if rx was rational, then it follows from Definition 1.12(M1), M(4) and M(5) that x = r...