# Math Help - Prove that lim sup(x_n) = max(lim sup(y_n), lim sup(z_n))

1. ## Prove that lim sup(x_n) = max(lim sup(y_n), lim sup(z_n))

Hi there, my first question here. Hope someone can give me some hints on it. Thanks!

Let $(x_{n})$ be a bounded sequence. For each $n \in \mathbb{N}$, let $y_{n}=x_{2n}$ and $z_{n}=x_{2n-1}$. Prove that
$\lim \sup {x_n} = \max (\lim \sup {y_n},\lim \sup {z_n})$

2. ## Re: Prove that lim sup(x_n) = max(lim sup(y_n), lim sup(z_n))

To show that $\limsup x_n = L$ (I'm using L to represent $\max(\limsup y_n,\limsup z_n)$), you need to show that $x_n < L$ for all n, and for every $\epsilon > 0$, there is an n such that $x_n > L-\epsilon$. Can you see how to show each part?

- Hollywood