\begin{definition}[Definition:Addition in Minimal Infinite Successor Set]
Let $\omega$ be the minimal infinite successor set.
The binary operation $+$ is defined on $\omega$ as follows:
:$\forall m,n \in \omega: \begin{cases} m + 0 &= m \\ m + n^+ &= \left({m + n}\right)^+\end{cases}$
where $m^+$ is the successor set of $m$.
This operation is called '''addition'''.
\end{definition}