Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $\text{Constant} \subseteq \text{Logarithmic}$?

share|improve this question
add comment

2 Answers 2

up vote 4 down vote accepted

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

share|improve this answer
add comment


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

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.