True or false under several conditions

Question

I want to check whether $$\max\bigl(0, x+\max(0, y+z-1)-1\bigr)=\max\bigl(0, z+\max(0, x+y-1)-1\bigr)$$ under restriction $x,y,z\in[0,1]$ but I don't know how to type it in WolframAlpha. For example this expression does not work:

  max(0, x+max(0, y+z-1)-1)=max(0, z+max(0, x+y-1)-1)  0<=x<= 1  0<=y<=1  0<=z<=1  true or false

Will be very grateful for help!

Answer 1

To find out all of the solutions:

It's a kinda magical fact that you can encode max and min into mathematical equations if you use absolute value. $$\max(a,b)=\frac{(a-b)+|a-b|}{2}+b$$

With this, you can write an (albeit complicated) equation that wolfram alpha will recognize.

To find out if $(x,y,z)$ is a solution for a particular set of values:

If you want to know if $(1/2,1/2,1/2)$ is a solution to the equation, you can type in

max(0, 1/2+max(0, 1/2+1/2-1)-1)=max(0, 1/2+max(0, 1/2+1/2-1)-1)

Directly and it is able to calculate that on my computer.