I'm playing with one of theorem in my notes:
Theorem
If a convergent sequence $\displaystyle\lim_{n\to\infty} = L$ that is bounded by $M$, then $|L| \leq M$
I wonder is there a connection between $L$ and $M$ if the sequence is non-decreasing? In other words, is it always true that $L = M$ for non-decreasing sequence that is bounded? I can't find a counterexampe, as well as a convincing arugment to connect $L$ and $M$. A hint would be greatly appreciated.