# Math Help - Real Analysis

1. ## Real Analysis

Let Xn be a series of real numbers. Show that lim (n going to infinity)inf (-Xn)=-lim (n going to infinity)sup Xn.

2. You have to show that $\liminf_{n\to \infty} \left(-x_n\right)= -\limsup_{n\to \infty} \left(x_n\right)$?
Use $\liminf_{n\to \infty}a_n = \sup_{n\in \mathbb N}\inf_{m\geq n}a_n$ and the result $\sup_k \left(-a_k\right) = -\inf_k\left(a_k\right)$

3. You must returen to :

Introduction To Real Analysis , By Robert Balrtle .