# What is the meaning of max() in intro. to algorithms?

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?

• Yes, it refers to the maximum of those two values. – Gokul Dec 10 '18 at 1:05

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.