Prove the following by induction (or otherwise):

[seeker101]

Does anyone have any suggestions on how to go about proving that

$$\left\lceil\frac{1}{2}{\lceil \log m\rceil}^2\right\rceil$$ is less than m-1, for m > 64? (using log to the base 2)

 

[CRGreathouse]

Prove that it's true for 64 < m <= 128, then use induction to show that it's true for ranges that are 2, 4, 8, ... times as large.

 

[seeker101]

Much appreciated!
Thank you.