I am trying to show the completeness of R, using the LUB property.
Problem is that I don't know, given a Cauchy sequence,where the limit would come from; I can check if a sequence {an} converges to a specific value, but I don't know how to come up with the limit value that the sequence would converge to.
I imagine as the intervals containing the terms am (m>N) become smaller, as |am-ak|N, maybe an converges to the limiting point of intervals (am,ak).
I used limsup and iminf to show that an converges , but this does not tell me what an should converge to.
Any Suggestions?