Structural Induction Set Example

Example

With a well-formed set of expressions comprised of:

• Variables $x,y,z,\dots$
• Operations $+,-,\times ,\dots$ Define the Alphabet for the expressions $\{x,y,z,+,-,x,÷,(,)\}$ Let $\mathcal{E}$ be the smallest set.

Base Case

Let our base case be $x,y,z\in \mathcal{E}$

Induction Step

Assume $e_1,e_2\in \mathcal{E}$ then, $(e_1+e_2),(e_1-e_2),(e_1\times e_2),(e_1÷e_2)\in \mathcal{E}$ …