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

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Continuity of T(n) for n≤2 is relevant when determining asymptotic bounds for recurrence relations. It suggests that T(n) may behave predictably in that range, potentially simplifying analysis. However, the Master Theorem does not typically account for this continuity in its application. Clarification on whether "continuous" was intended to mean "constant" for n≤2 is also discussed. Understanding these nuances is crucial for accurate asymptotic analysis.
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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?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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