What Does the Function Notation U(x_0, x_1, ..., x_n) Indicate?

[Cinitiator]

Homework Statement

What does this notation mean? I understand the $$\{x_t\}_{t = 0}^{\infty}$$ part, but I don't know what exactly $$U(x_0, x_1, ... x_n)$$ means. Does it mean that this function is a n+1 dimensional function, the same way f(x, y) is a 3 dimensional function?

Homework Equations

$$U(\{x_t\}_{t = 0}^{\infty}) = U(x_0, x_1, x_2, ... x_n)$$

The Attempt at a Solution

Tried Googling without any luck.

 

[I like Serena]

Hi Cinitiator!

but I don't know what exactly $$U(x_0, x_1, ... x_n)$$ means. Does it mean that this function is a n+1 dimensional function, the same way f(x, y) is a 3 dimensional function?

Yep.
That's it!Slightly sharper: f(x,y) is a function of 2 dimensions.
And if f(x,y) yields a real number as its value, it defines a graph in 3 dimensions.

$U(x_0, x_1, ... x_n)$ is a function of (n+1) dimensions (don't forget to count 0).
It will define a graph in (n+2) dimensions.