Definition:Addition in Minimally Inductive Set

Definition
Let $\omega$ be the minimally inductive set.

The binary operation $+$ is defined on $\omega$ as follows:


 * $\forall m, n \in \omega: \begin {cases} m + 0 &= m \\ m + n^+ & = \paren {m + n}^+ \end {cases}$

where $m^+$ is the successor set of $m$.

This operation is called addition.

Also see

 * Addition in Minimally Inductive Set is Well-Defined