tend to zero as the index grows. However, with growing values of , the terms become arbitrarily large. So, for any index and distance , there exists an index big enough such that As a result, no matter how far one goes, the remaining terms of the sequence never get close to ; hence the sequence is not Cauchy.
tend to zero as the index grows. However, with growing values of , the terms become arbitrarily large. So, for any index and distance , there exists an index big enough such that As a result, no matter how far one goes, the remaining terms of the sequence never get close to ; hence the sequence is not Cauchy.