Analysis 1A — Supremum Example

Christian Jones: University of Bath

October 2023

Question

Here is an example of finding the supremum of a set taken from an old problem sheet, together with three possible methods to find it.

Example 1:

Let \[B = \left\lbrace \frac{2n-1}{n+1} \lvert n \in \mathbb{N}\right\rbrace.\] Show that \(B\) is bounded above and find \(\sup(B).\)