Talk:Cauchy Sequence is Bounded/Real Numbers

Why do you need to prove anything for less than $N$? The definition of a Cauchy sequence says nothing about the behaviour of a sequence for $m, n$ less than $N$, so there should be no need to address that case, surely? What am I missing? --prime mover (talk) 08:57, 26 August 2017 (EDT)


 * It's just a completeness thing, without taking for granted that unboundedness can only occur on the infinite end of the sequence. So just to construct an explicit bound for the absolute values and prove it bounded explicitly. &mdash; Lord_Farin (talk) 10:15, 26 August 2017 (EDT)


 * I have same opinion with Lord_Farin and I also think it is better to introduce $\epsilon$ rather than 1. Because by introducing $\epsilon$ we can show explicitly the tight bound for the given sequence. --Bltzmnn.k (talk) 11:51, 26 August 2017 (EDT)