For $(3n)$, how would I prove that the limit of $n$ approaching infinity does not exist? Obviously this would diverge but I'm not completely sure how to prove it. I know I have to use epsilon delta.
2026-04-02 20:53:15.1775163195
Epsilon Limit Proof (Bridge to Abstract Mathematics)
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Let $\epsilon > 0$. Let $3n < \epsilon$. By the Archimedean property there exists an $n + \delta$ such that $3(n + \delta) > \epsilon$. Note that $\delta$ is a positive integer.