Prove that $$\limsup(a+b) \leq \limsup(a) + \limsup(b)$$ and $$\liminf(a+b) \geq \liminf(a) + \liminf(b)$$ where $a,b:\mathbb{N}\to \mathbb{R}$ are two bounded sequences.
I'm not sure where to begin on this proof.
2026-03-29 05:58:45.1774763925
Prove that $\limsup(a+b) \leq \limsup(a) + \limsup(b)$ and $\liminf(a+b) \geq \liminf(a) + \liminf(b)$
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