Is there any notation for referring to a general set of $N$ elements? Currently I'm using $\{1, \dots, N\}$, but the fact that the set consists of natural numbers is irrelevant. I'd prefer to just write something like ${\mathfrak{S}}(N)$. :-)
For instance, I know natural numbers are some times encoded as $0 = \{\}$, $1 = \{0\}$, $2 = \{0, 1\}$. The $N$:th element in such encoding could for instance do.