Let $(p_n)$ be a sequence with real numbers such that $\liminf (p_n)=-10$ and $\limsup (p_n)=10$. Now, are the following questions true or not true. (Prove answers). 1.)The sequence $(p_n)$ does not converge. 2.) That $(p_n)$ is both monotone increasing/decreasing. 3.) That $(p_n)$ is bounded.
1.)We know $(p_n)$ does not converge $\liminf\neq \limsup$.
3.) Since liminf and limsup $\neq$ to either $\infty$ or $-\infty$ we know $(p_n)$ is bounded.
Are my 1.) and 3.) right??? and can i get help on 2 please!