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Small problem

  1. Jan 1, 2008 #1
    Hey i was wondering if someone could help me express this using standard binary operators.

    [tex]f(x,y,z)=\frac{max(0, (x-y) )}{z}[/tex]

    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. jcsd
  3. Jan 2, 2008 #2
    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)

    [tex]
    f: \mathbb{R} \times \mathbb{R} \times \mathbb{R} \backslash \{0\} \to \mathbb{R}[/tex]
    [tex]

    f(x,y,z) = \left\{
    \begin{array} {l l}
    \displaystyle{\frac{x-y}{z}} & \text{if} \ x > y \\
    0 & \text{else}
    \right.
    [/tex]
     
  4. Jan 2, 2008 #3
    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.
     
  5. Jan 2, 2008 #4
    How about

    [tex]\frac{|x-y|+(x-y)}{2z}[/tex]
     
  6. Jan 2, 2008 #5
    ok, now i need to express that without the absolute function, or using polar or complex numbers. Could take me all week.....
     
  7. Jan 2, 2008 #6
    For the absolute value you could use [tex]\sqrt {(x - y)^2}[/tex] (I smell a computer nearby), but it looks like on overshoot to me.
     
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