Inductive Definition

logic

Definition

Inductive Definition

Inductive definitions are used to construct infinite sets based on the definition rules.

Example: Let $\mathbb{A}$ denote an alphabet and $\mathbb{T}$ denote the possible words, then:

1. $\alpha \in \mathbb{A}⟹[aa]\in \mathbb{T}$.
2. $a,b\in \mathbb{A}\wedge [aa]\in \mathbb{T}⟹[aba]\in \mathbb{T}$.

Using these definitions rules, a set of possible words can be inductively (iteratively) created.