- #1
Mr Davis 97
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I have a question, not based on any homework but just based on my own readings. If ##L \in \mathbb{R}## and ##L>0##, and if ##\lim a_n < L##, does there necessarily exist an ##N \in \mathbb{N}## such that ##a_N < L##? How would I prove this if its true? I tried to use the definition of convergence but got nowhere. I guess this statement could also be false but I couldn't find a counter example...