Lemma 4.2. 1101/If an is a rational Cauchy sequence which does not tend to 0, then there enst a positive EQ and no EN such that either Solution proof is simply by the definition of cauchy sequence . if the sequence does converge to zero then there exist such delta such that an is < delta for every n >= N. The statment is just the contraposition of the statemen.

1. Lemma 4.2. 1101/If an is a rational Cauchy sequence which does not tend to 0, then there enst a
positive EQ and no EN such that either
Solution
proof is simply by the definition of cauchy sequence . if the sequence does converge to zero then
there exist such delta such that an is < delta for every n >= N. The statment is just the
contraposition of the statemen