\begin{definition}[Definition:Disjunction/General Definition]
Let $p_1, p_2, \ldots, p_n$ be statements.
The '''disjunction''' of $p_1, p_2, \ldots, p_n$ is defined as:
:$\ds \bigvee_{i \mathop = 1}^n \ p_i = \begin{cases}
p_1 & : n = 1 \\
& \\
\ds \paren {\bigvee_{i \mathop = 1}^{n - 1} \ p_i} \lor p_n & : n > 1
\end{cases}$
That is:
:$\ds \bigvee_{i \mathop = 1}^n \ p_i = p_1 \lor p_2 \lor \cdots \lor p_{n - 1} \lor p_n$
In terms of the set $P = \set {p_1, \ldots, p_n}$ this can also be rendered:
:$\ds \bigvee P$
and is referred to as the '''disjunction of $P$'''.
\end{definition}