Algebraic Formula of max Function

One-minute read
Sparisoma Viridi
function • algebraic • conditional

A function to select maximum value between two of its arguments can have algebraic form

max⁡(x,y)=x+y+∣x−y∣2(1)\tag{1} \max(x, y) = \frac{x + y + |x - y|}{2}

as alternatif to the common form

max⁡(x,y)={x,x≥y,y,x<y.(2)\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)) \max(a, b, c) = \max(a, \max(b, c))

is for a function with a three arguments.