A function to select maximum value between two of its arguments can have algebraic form
$$\tag{1} \max(x, y) = \frac{x + y + |x - y|}{2} $$
as alternatif to the common form
$$\tag{2} \max(x, y) = \left\{ \begin{array}{cc} x, & x \ge y, \newline y, & x < y. \end{array} \right. $$
The functions can be extended to function with more arguments, e.g.
$$ \max(a, b, c) = \max(a, \max(b, c)) $$
is for a function with a three arguments.
- Paul Sinclair, “Answer to ‘Function Equivalent to the Maximum Operator?’”, Mathematics Stack Exchange, 5 Feb 2016, url https://math.stackexchange.com/a/1641271/645927 [20221124].