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Let's say we have two "Big-Oh" sets called $\text{Constant}$ and $\text{Logarithmic}$, such that one has $O(1)$, and the other has $O\big(\log(n)\big)$, respectively, how would I show that $\text{Constant} \subseteq \text{Logarithmic}$?

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up vote 4 down vote accepted

Higher order set contains lower order set. In your case $\lim \limits_{n\rightarrow \infty}\frac{\log n}{1}=\infty.$

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Hint:

Logarithms are increasing and unbounded. But a constant is bounded.

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