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I'm reading chapter 3(growth functions) of CLRS and in giving an example of proving theta for a standard quadratic function the book gives the following value for $n_0 = 2 \cdot max(|b|/a, \sqrt{|c|/a})$ .

I'm confused regarding what "max" means in this context. The quadratic function is $an^2 + bn + c$ and the constants give are $c_1 = a/4, c_2 =7a/4$.

I'm thinking it might mean which ever of the parameters yields a larger value?

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  • $\begingroup$ Yes, it refers to the maximum of those two values. $\endgroup$
    – Gokul
    Dec 10, 2018 at 1:05

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Yes, as confirmed by Gokul, $\max(p,q)$ just means the larger one of its two parameters, $p$ and $q$. It can also apply to more parameters such as $\max(p, q, r, s, t)$, where it means the largest of all 5 variables or values.

Its opposite is $\min$, which is used in the same way but means the smaller one of two values or the smallest one of all given values.

You might want to check the list of mathematical abbreviations the next time you get confused by some math abbreviations.

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