What is the notation for a set with a variable size?

Question

I'm trying to write the definition "Set $S$ has between $0$ and $n$ elements (inclusive)" concisely in set notation.

For the case when $n=4$, I would write the definition as $$S=\{\}\vee \{a\}\vee \{a, b\}\vee \{a, b, c\}\vee \{a, b, c, d\}$$ but this obviously doesn't scale to arbitrary $n$.

Answer 1

You could write $0\le|S|\le n$ to indicate that the set $S$ has between $0$ and $n$ elements (inclusive). $|S|$ denotes the cardinality of the set $S$.