I need some help with limsup. I need some help with limsup. @Mathematics

Question

anonymous · Answer

I'm trying to prove $\limsup (a_{n} + b_{n}) \leq \limsup a_{n} + \limsup b_{n}$

anonymous · Answer

The definition I'm trying to work with is that the $\limsup s_{n}$ is the largest $M$ such that there are $\infty$ly many $s_{n} > M - \varepsilon$ for all $\varepsilon > 0$.

anonymous · Answer

Be I keep coming up with if $\alpha = \limsup a_{n}$ and $\beta = \limsup b_{n}$, then there are $\infty$ly many $a_{n} > \alpha - \varepsilon$ and $\infty$ly many $b_{n} > \beta - \varepsilon$

anonymous · Answer

Figured out my problem.  The $n$ don't have to be the same.  Thanks for listening!