The terminology "G is only a function of...."

[Stephen Tashi]

TL;DR

For example, if we have a set of variables x1, x2,...xn, what does it mean to say "G is only a function of x1,x2,x3"?

If we have a set of variables $x_1, x_2, ...x_n$ what does it mean to say that "$G$ is only a function of $x_1,x_2,x_3$"?

My thoughts:

Context 1: The function $G$ has been previously defined.

In Context 1, saying "$G$ is only a function of $x_1,x_2,x_3$" means the same thing as the usual interpretation of "$G$ is a function of $x_1,x_2,x_3$ , namely that $\{x_1,x_2,x_3\}$ is exactly the set of arguments for $G$ ( rather than being a proper subset of the arguments for $G$).

Context 2: $G$ represents the measurement of some physical phenomenon such as temperature or speed.

Possibiity 2 a) $G$ can be expressed as a function of $x_1,x_2,x_3$ However $G$ might be constant with respect to some of those variables.

Possibility 2 b) $G$ can be expressed as a function of $x_1,x_2,x_3$ and $G$ is not constant with respect to any of those variables.

I think possibility 2 b) is the most common interpretation.

 

[mathman]

My vote - 2a).

 

[mfb]

Possibility 3) G does not depend on x₄ to x_n.

You would typically expect it to be not constant with respect to x₁ to x₃ everywhere (but it might still be constant with respect to these in some regions of the domain).

 

[nuuskur]

Declare simply $G=G(x_1,x_2,x_3)$ and that's the end of it. If we say it only depends on these variables, that's going to open another can of worms. E.g if $G$ was almost constant w.r.t some variable, in some contexts it could be viewed as NOT being dependent on that variable. Keep it simple, be precise.