Exercise 2.6.5. If (rn) and (yn) are Cauchy sequences, then one easy way to prove that (n + Yn) is Cauchy is to use the Cauchy Criterion. By Theorem 2.6.4, (n) and (yn) must be convergent, and the Algebraic Limit Theorem then implies (n + yn) is convergent and hence Cauchy. (a) Give a direct argument that (n + yn) is a Cauchy sequence that does not use the Cauchy Criterion or the Algebraic Limit Theorem. (b) Do the same for the product (nyn).