Confused about simple max{,} notation

In summary, the max{f(x,Z), g(x,Z)} notation represents the largest value between two known functions, f and g, when the condition Z > 10 and f(x,Z) < 2 is met. It is a function that determines the larger value between f and g for a given value of x. Examples were provided to further illustrate this concept.
  • #1
dtessela
2
0
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!

D
 
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  • #2
dtessela said:
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!

D

It's the largest value of f and g, where Z > 10 and f(x, Z) < 2.
 
  • #3
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)
 
  • #4
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.
 
  • #5
HallsofIvy said:
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.

Thanks, that helped clear it up!
 

1. What is the meaning of "max" in mathematical notation?

In mathematics, "max" is shorthand for "maximum" and represents the largest value in a set of numbers or the greatest possible value of a function.

2. How is "max" notation used in scientific research?

"Max" notation is commonly used in scientific research to represent the maximum value of a variable or parameter in a given system or experiment. It is often used to determine the upper limit or threshold of a certain phenomenon.

3. Can "max" notation be used with more than two numbers?

Yes, "max" notation can be used with any number of numbers. For example, "max{4, 7, 9, 2, 5}" would represent the largest value among the numbers 4, 7, 9, 2, and 5.

4. What is the difference between "max" and "max{" notation?

"Max" notation without the curly braces is typically used to represent the maximum value of a function or equation, while "max{" notation is used to represent the maximum value within a set or list of numbers.

5. Can "max" notation be used to find the minimum value?

No, "max" notation specifically represents the maximum value. To find the minimum value, "min" notation would be used instead.

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