I have a question that states:

Let $f(n), g(n), h(n)$ be positive, monotonically non-decreasing functions. Prove or disprove:If $f(n), g(n) = Θ(h(n))$ then $\frac{f(n)}{g(n)} = Θ(1)$.

So, if $f(n) = \Theta(h(n))$, then the reverse is true, right? Which means that $f(n) = \Theta(g(N))$ and vice versa, which would of course make the growth of f(n) and g(n) equal. Dividing them would give you 1. This is a valid statement, no?


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