Prove the following by induction (or otherwise):

Thread starter seeker101
Start date Aug 14, 2010
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Induction

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The discussion focuses on proving that the expression ⌈(1/2) * (⌈log2 m⌉)^2⌉ is less than m - 1 for m > 64. Participants suggest starting with a base case for the range 64 < m ≤ 128 and then applying mathematical induction to extend the proof to larger ranges that double in size. The importance of using the properties of logarithms and ceiling functions in the proof is emphasized. The goal is to establish the inequality holds for progressively larger values of m. This approach aims to provide a comprehensive proof through induction.

Aug 14, 2010

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)

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Aug 14, 2010

CRGreathouse

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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.

Aug 15, 2010

seeker101

Much appreciated!
Thank you.

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