Elementary Set Theory – Notation for Finite Subsets of Natural Numbers

Question

Is there a "standard" notation to denote the set of all finite subsets of $\mathbb{N}$?
(or any set, not just $\mathbb{N}$)

Thanks

Answer 1

Several possible notations for $\{A\subseteq\omega\mid |A|<\omega\}$:

1. $[\omega]^{<\omega}$
2. $P_\omega(\omega)$
3. $\operatorname{Fin}(\omega)$

Where, of course, $\omega=\mathbb N$.

And as usual my advice on the matter: When in doubt, open with "We denote by [the chosen notation here] the set ..."