Find the mistakes in the “proofs” that the sum of any two rational numbers is a rational n...

Find the mistakes in the “proofs” that the sum of any two rational numbers is a rational number.

Exercise

“Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b ≠ 0, and s = a/b for some integers a and b with b ≠ 0. Then

Let p = 2a. Then p is an integer since it is a product of integers. Hence r + s = p/b, where p and b are integers and b ≠ 0. Thus r + s is a rational number by definition of rational. This is what was to be shown.”