What is the proper terminology / symbol to use for a function that reaches some point/value or a variable? Not necessarily converge to it, but passes it somehow?
Example
For $x\in\mathbb{N}$. Set initially $x_0=2$.
Iterating the function $f(x) = 2x$ will at some point reach the value $64$ for example: $\{4,8,16,32,\underline{64},128,256,..\}$. For this case, $f(x)$ passes $x_0^6$ ? (i.e. $x_0$ raised to $6$).
Or do you say, for some $n$ the function $f^n(x)$ will reach or pass the value $64$ or $x_0^6$?
If we use two functions, is it possible to say the function $f^n$ passes through function $g^n$ at some $n$? or $f^n = g^n$ at some $n$ ?
To answer the question in the body, we say that "$64$ is in the orbit of $2$ under $f$".
More generally, if $f^n(x_0)=y$, then say that "$y$ is in the orbit of $x_0$ under $f$".