I am new to this forum so please bear with me if I miss any information. I am currently taking advanced calculus using the textbook Introduction to Analysis (5th Ed) by Edward Gaughan. I am having a lot of trouble answering the following question:
Assume that $\{a_n\}^∞_{n=1}$ is a sequence of positive real numbers converging to $L > 0$. Prove that there is a positive real number $m$ such that $a_n ≥ m$ for all $n ∈\Bbb N$.
Scratch work for proof:
I tried to go to my professor for help and he said I need to solve for an actual number of $m$ and needed to used bounds. As he went to into more detail, I ended up getting even more confused.
This is my second proofs class, and it is a subject I have been known to struggle with. I really am trying to get better at it so any tips or advice on how to solve this would be helpful.