Title pretty much says it all. I would think this should be true, but don't have much experience in this area of mathematics and don't know how to go about proving it.
2026-04-07 06:16:13.1775542573
Is $f(n)=\Theta(g(n))$ equivalent to the existence of the limit $\lim_{n \to \infty} \frac{f(n)}{g(n)}$?
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No. For example, $2 + \sin(n) = \Theta(1)$.