Definition:Addition in Minimally Inductive Set

Definition
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.

Also see

 * Addition in Minimal Infinite Successor Set is Well-Defined