# Math Help - convergence

1. ## convergence

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

2. Originally Posted by janae77
Construct a sequence { $x_{n}$} of reals such that a = $\sup{x_{n}:n\in N}$ exists, a is not the limit of $x_{n}$ and for every $\epsilon\ge 0$ and k a positive integer, there exists a positive integer N greater than k such that the absolute value of ( $x_{N}-a$) is less than $\epsilon$
Simplest example: $x_n=(-1)^n$