I understand that Kleene star is defined as:
$$V^*=\bigcup_{i = 0 }^\infty V_i = V_0 \cup V_1 \cup V_2 \cup V_3 \cup \ldots.$$
(given $V$ is a formal language, $V_0 = \{\varepsilon\}$, and $V_k$ is a concatenation of V with itself k times, I saw it in some places notated also as $V^k$ so I thought it's worth clarifying)
So if $V = \{a,b,c\}$, then $V^*$ is basically the regex equivalent of [abc]*, meaning "all possible strings containing 'a','b' or 'c' or the empty string of any length".
My question is a little naive and coming from Regex. Is there a notation for "all possible strings containing 'a','b' or 'c' or the empty string up to length $n$"?
E.g. in regex it would be: [abc]{0,n} where n is the max length of a word
Is there a an equivalent mathematical notation for this?
e.g. what is the operator on V that means this:
$$V^{\mathrm{something\ like}\{0,n\}?}=\bigcup_{i = 0 }^n V_i = V_0 \cup V_1 \cup \ldots \cup V_n$$
Edit.
You can find two notations in the literature. The notation $V^{\leqslant n}$, suggested by Zhen Lin and the notation $(1 + V)^n$ (or $(1 \cup V)^n$ if you prefer the union symbol). The latter one does not need to introduce any definition, but the first one is rather intuitive.