Joined successions A succession (an) of genuine number is known as a focalized arrangements if a keeps an eye on a limited breaking point as n→∞. On the off chance that we say that (a) has a breaking point a∈ F if given any ε > 0, ε ∈ F, k∈ â„• | a – a | < ε n ≥ k In the event that a has a farthest point an, at that point we can compose it as liman = an or (a) → a. Cauchy Sequence A Cauchy succession is an arrangement in which numbers turn out to be nearer to each different as the grouping advances. On the off chance that we say that (an) is a Cauchy succession if given any ε > 0, ε ∈ F, k∈ â„• | a – am | < ε n,m ≥ k. Gary Sng Chee Hien, (2001). Limited sets, Upper Bounds, Least Upper Bounds A set is called limited if there is a sure feeling of limited size. A set R of genuine numbers is called limited of there is a genuine number Q with the end goal that Q ≥ r for all r in R. the number M is known as the upper bound of R. A set is limited in the event that it has both upper and lowe>