Is there a notation for being "a finite subset of"? I would gladly use a notation for “$A$ is a finite subset of $B$”, like 
$$A\sqsubset B \text{ or } A\underset{fin}{\subset} B,$$ 
but I have never seen a notation for that. Are there any?

EDIT: While waiting for a future standard, I will use Joffan’s $\ddot{\subset}$ coded as  
$\newcommand{\finsub}[0]{\mathrel{\ddot{\subset}}}$
$A\finsub B$

$\newcommand{\finsub}[0]{\mathrel{\ddot{\subset}}}$
I will paste the new command in the first row, and then use \finsub, resulting in $A\finsub B$ which I will explain after first use in each text. I guess that is satisfying enough.
And really, as you define sets and functions in a text, you could as well define relations without standard notations.

There are two options:


*

*You use the notation often. Then define it properly at the beginning (or when you first need it) and use whatever you think is reasonable. I'd suggest, as others:
$$ A \subset_{\mathrm{fin}} B, \quad A \sqsubset B, \quad A \mathrel{\ddot{\subset}} B, \quad  A \subset\!\!\!\!\!\cdot\!\!\cdot\, B \quad \ldots $$

*You use it one or twice. Then just spell it out:


*

*... where $A\subset B$ is finite

*... $(\forall A \subset B, \, A\text{ finite})$

*...



Of course, you can use $|A|<\infty$ or $|A|<|\mathbb N|$ or $|A|<\omega$ or whatever, just try to imagine being a reader of your text and think what is the least confusing thing.
