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. If r + s is rational, then by definition of rational r + s = a/b for some integers a and b with b ≠ 0. Also since r and s are rational, r = i/j and s = m/n for some integers i, j, m, and n with j ≠ 0 and n ≠ 0. It follows that

which is a quotient of two integers with a nonzero denominator. Hence it is a rational number. This is what was to be shown.”