Let $\{x_n\}$ be a sequence such that $$ \limsup_n x_n\leq M<\infty $$ Can we say theres exist a subsequence $\{y_{n}\}$ of $\{x_n\}$ such that $$ y_{n}\leq y_{n+1}\qquad \forall n $$ And $$ y_n\leq M\qquad \forall n $$
2026-03-28 16:14:12.1774714452
If $\limsup_n x_n\leq M$ then there exists a subsequence $\{y_{n}\}$ such that $ y_{n}\leq y_{n+1}$ and $ y_n\leq M$, $\forall n $
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