Are The Reals Compact? The set R of all real numbers is not compact as there is a cover of open intervals that does not have a finite subcover. For example, intervals (n−1, n+1) , where n takes all integer values in Z, cover R but there is no finite subcover. … In fact, every
How Do You Prove Monotone? if an ≥ an+1 for all n ∈ N. A sequence is monotone if it is either increasing or decreasing. and bounded, then it converges. How do you prove a sequence is monotone? if an ≥ an+1 for all n ∈ N. A sequence is monotone if it is either
How Do You Know If A Sequence Is Monotonic? If {an} is an increasing sequence or {an} is a decreasing sequence we call it monotonic. If there exists a number m such that m≤an m ≤ a n for every n we say the sequence is bounded below. The number m is sometimes called a