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.

For $n \in \mathbb{Z}^+$, given any function $T(n)$ such that $T(n) = \Omega(n^3)$ and $T(n) = O(n^4)$, how can I prove that constants $C$ and $N$ exist such that

$$ n^3 + 10 \le CT(n) \le n^4 $$

for all $n > N$?

My initial attempts have stemmed from the definitions of big-O. We can definitely prove that there exists constants such that:

$$ C_1(n^3 + 10) \le T(n) \le C_2n^4 $$

for all $n > N'$, but I can't compute a single constant $C$ that would work for the first inequality.

share|improve this question

1 Answer 1

The assertion is wrong. Try $T(2n)=n^3$ and $T(2n+1)=3n^4$.

share|improve this answer

Your Answer

 
discard

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.