Discrete Math - Strong Induction Question

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SUMMARY

The discussion centers on a strong mathematical induction problem, specifically addressing the transition from 44/49 to 49/49 in the proof process. The participant seeks clarification on the logic behind this step, asserting that if a > 0, then a*(44/49) is less than a*(49/49), which aligns with the properties of strictly increasing functions. The explanation hinges on understanding the implications of multiplying by a positive constant in the context of inequalities.

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Homework Statement


Prove by Strong Mathematical Induction[/B]
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Homework Equations


N/A

The Attempt at a Solution


The steps to solving this problem are shown below. I understand all steps of the problem until the part where it says 44/49 becomes 49/49 since 44 < 49. Can someone please explain the logic behind that step? Thank you.
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Last edited:
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If a>0 then a*(44/49) < a*(49/49).
Sort of like saying that f(x) = ax is strictly increasing.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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