Confused about simple max{,} notation

  1. I'm working on a project that required me to go through the literature to find some information on Compton and Rayleigh scattering. I came across a key expression, part of it which read:

    max{ f(x,Z), g(x,Z) } if Z > 10 and f(x,Z) < 2

    where f(x,Z) and g(x,Z) are known functions.
    The problem is I don't understand the max{f(x,Z),g(x,Z)} notation. I have done some poking around on the interwebs but nothing really helpful has come up.

    Thanks for future help!

  2. jcsd
  3. Mark44

    Staff: Mentor

    It's the largest value of f and g, where Z > 10 and f(x, Z) < 2.
  4. Here are some examples for you:

    max{10, 3} = 10
    max{-1, -100} = -1

    if x = 30*3 and y = 40! and z = 40^2

    then max{x, y, z} = y

    if f(x) = 2x + 10 and g(x) = x^3

    then when x = 1

    max{f(x), g(x)} = f(x)
  5. HallsofIvy

    HallsofIvy 41,259
    Staff Emeritus
    Science Advisor

    Notice that max{a, b} applied to numbers a and b. max{f(x), g(x)} is actually a function, h(x), that, to each value of x, gives the larger of the two numbers f(x) and g(x) for that particular x.
  6. Thanks, that helped clear it up!
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