# Small problem

1. Jan 1, 2008

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.

2. Jan 2, 2008

### 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)

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

3. Jan 2, 2008

hmm yeah, thats 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.

4. Jan 2, 2008

### d_leet

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

5. Jan 2, 2008

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