How Does Continuity of T(n) for n≤2 Impact Asymptotic Bounds?

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SUMMARY

The discussion centers on the impact of the continuity of the recurrence relation $T(n)$ for $n \leq 2$ on determining asymptotic bounds. Participants clarify that the continuity likely implies constancy in this range, which is crucial for applying the Master Theorem. It is established that this continuity does not influence the application of the Master Theorem directly. The key takeaway is understanding how the behavior of $T(n)$ in the interval affects asymptotic analysis.

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evinda
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Hello! (Wave)I am given some recurrence relations $T(n)$ and I have to give asymptotic upper and lower bounds for $T(n)$.
We assume that $T(n)$ is continuous for $n \leq 2$.
How can we use the fact that $T(n)$ is continuous for $n \leq 2$? (Thinking)
 
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Probably meant "constant for $n \leq 2$".
 
Bacterius said:
Probably meant "constant for $n \leq 2$".

Nice, thank you! (Smile)

We don't take this fact into consideration when we use the Master Theorem, right?
 

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