How to express $\max\{a,b,c\}$

Question

We know 2 $\max\{a,b\}=a+b+|a-b|$, is there any similar formular about $\max\{a,b,c\}$? How about $\max\{x_1,x_2,\cdots,x_n\},$ where each $x_i$ is a real number ?

Answer 1

Hint $$\max\{a,b,c\}= \max\{\max\{a,b\},c\}$$

Use the formula for two numbers twice. Similarly

$$\max\{x_1,x_2,\cdots,x_n\}=\max \{ \max\{x_1,x_2,\cdots,x_{n-1}\}, x_n \}$$

which gives a recursive formula..