Eliminating arguments from a function

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As the conversation involves thermodynamics and mathematics, the question is asking for a more rigorous explanation of a concept related to the zeroth law of thermodynamics and empirical temperature. Specifically, it is asking how to show that given certain conditions, there exist functions g1 and g2 that are independent of z and can be used to represent f1 and f2. This can be achieved by reducing f1 and f2 to be independent of z, and using those reduced versions as g1 and g2.
  • #1
thegreenlaser
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My issue comes from thermodynamics (https://www.physicsforums.com/threads/zeroth-law-of-thermodynamics-and-empirical-temperature.774255/), but I guess this is really a math problem rather than a physics problem:

Let [itex] \boldsymbol{x} \in \mathbb{R}^m [/itex], [itex] \boldsymbol{y} \in \mathbb{R}^n [/itex], [itex] \boldsymbol{z} \in \mathbb{R}^p [/itex].

Given
[tex] f_1 (\boldsymbol{x}, \boldsymbol{z} ) = f_2 (\boldsymbol{y}, \boldsymbol{z}) [/tex]
and
[tex] f_3(\boldsymbol{x}, \boldsymbol{y}) = 0, [/tex]
how can we show that there exist functions [itex] g_1, g_2 [/itex] such that
[tex] g_1(\boldsymbol{x}) = g_2(\boldsymbol{y}) [/tex]

(i.e., [itex] f_3 = 0 [/itex] means that [itex] f_1 [/itex] and [itex] f_2 [/itex] can be reduced so they're independent of [itex] \boldsymbol{z} [/itex])

In my physics class, we were given a sort of "hand-waving" argument, but I'm having trouble finding a more rigorous explanation. Can anyone help me out?
 
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  • #2
I have trouble understanding the question, but I'll take a stab at it. The last comment says f1 and f2 can be reduced to be independent of z. In that case wouldn't g1 and g2 simply be these reduced versions of f1 and f2?
 

FAQ: Eliminating arguments from a function

What does it mean to eliminate arguments from a function?

Eliminating arguments from a function refers to the process of simplifying or reducing the number of variables or inputs that are required for a function to run. This can make the function more efficient and easier to understand.

How can eliminating arguments improve a function?

By reducing the number of arguments, a function can become more streamlined and easier to use. This can also make the code more readable and less prone to errors or bugs. Additionally, eliminating arguments can make a function more reusable, as it may not be dependent on specific inputs.

What are some common techniques for eliminating arguments from a function?

There are several techniques that can be used to eliminate arguments from a function, including partial application, currying, and using default values for arguments. These techniques can help simplify the function and make it more flexible.

Are there any potential drawbacks to eliminating arguments from a function?

While eliminating arguments can have many benefits, it can also make a function less versatile. By reducing the number of arguments, the function may be limited in its functionality and may not be able to handle certain scenarios. Additionally, eliminating arguments may make the code less self-documenting, as it may not be immediately clear what inputs are required for the function to run.

When is it appropriate to eliminate arguments from a function?

Eliminating arguments from a function can be useful in many situations, but it is not always necessary or appropriate. It is generally best to eliminate arguments when they are not needed or when they can be replaced with a more efficient approach. For example, if a function has a default value for an argument that is rarely changed, it may be beneficial to eliminate that argument to simplify the function.

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