Definition:Recursively Defined Mapping/Minimally Inductive Set
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Definition
Let $\omega$ be the minimally inductive set.
Let $T$ be a set.
Let $a \in T$.
Let $g: T \to T$ be a mapping.
Let $f: \omega \to T$ be the mapping defined as:
- $\forall x \in \omega: \map f x = \begin{cases} a & : x = 0 \\ \map g {\map f n} & : x = n^+ \end{cases}$
where $n^+$ is the successor set of $n$.
Then $f$ is said to be recursively defined on $\omega$.