Solving a max() Function with Binary Operators

[Barking_Mad]

Hey i was wondering if someone could help me express this using standard binary operators.

$$f(x,y,z)=\frac{max(0, (x-y) )}{z}$$

i.e. Eliminate the max() function and write it using proper math.

EDIT: max(a,b) simply chooses the largest value of the two variables.

 

[LukeD]

What you have there already is valid, but you can use this one if you like it better

Also, note that z cannot be 0 (the first line is just declaring the domain and codomain of f)

$$f: \mathbb{R} \times \mathbb{R} \times \mathbb{R} \backslash \{0\} \to \mathbb{R}$$
$$<br /> f(x,y,z) = \left\{<br /> \begin{array} {l l}<br /> \displaystyle{\frac{x-y}{z}} & \text{if} \ x > y \\<br /> 0 & \text{else}<br /> \right.$$

 

[Barking_Mad]

hmm yeah, that's not exactly what i was looking for, apologies for lack of clarity.

Im looking for an algebraic expresion of that function, as a fraction or something similar, without the need to use if or else. If that is possible, maybe it isnt.

 

[d_leet]

How about

$$\frac{|x-y|+(x-y)}{2z}$$

 

[Barking_Mad]

ok, now i need to express that without the absolute function, or using polar or complex numbers. Could take me all week...

 

[dodo]

For the absolute value you could use $$\sqrt {(x - y)^2}$$ (I smell a computer nearby), but it looks like on overshoot to me.