Construct a sequence {$\displaystyle x_{n}$} of reals such that a = $\displaystyle \sup{x_{n}:n\in N}$ exists, a is not the limit of $\displaystyle x_{n}$ and for every $\displaystyle \epsilon\ge 0$ and k a positive integer, there exists a positive integer N greater than k such that the absolute value of ($\displaystyle x_{n}-a$) is less than $\displaystyle \epsilon$