\begin{definition}[Definition:Normal Series/Infinite]
A normal series may or may not terminate at either end:
:$\cdots \stackrel {\phi_{i - 1} } {\longrightarrow} H_{i - 1} \stackrel {\phi_i} {\longrightarrow} H_i \stackrel {\phi_{i + 1} } {\longrightarrow} H_{i + 1} \stackrel {\phi_{i + 2} } {\longrightarrow} \cdots$
Such a series is referred to as an '''infinite normal series'''.
The context will determine which end, if either, it terminates.
\end{definition}