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!

Do you want to know if this holds for all $(x,y,z)$, a particular triplet, or code that will check it for all triplets? — Stella Biderman, Apr 16 '16 at 14:16
I know that. That doesn't answer my question. What kind of answer do you want — Stella Biderman, Apr 16 '16 at 14:43
I am do not exactly understand what triplet means. I just whant to check wheather this equality holds when my variables satisfy described condition. — Bogdan, Apr 16 '16 at 14:44
A triplet is just a set of three variables. So you want to be able to check if it holds, for any set of three variables that meet your criterion. — Stella Biderman, Apr 16 '16 at 14:45

score 1 · Accepted Answer · answered Apr 16 '16 at 14:55

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.

Thank you very much for answer the question as well as for additional useful information! — Bogdan, Apr 16 '16 at 18:04

True or false under several conditions

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