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- MAT102 Prep 9

Recursion in Math

Definition

This is the process of creating new elements from existing elements in a set.
There are always the:
- Basis:
  - The set of elements which are assumed to be in the set at the start.
- Constructor:
  - A collection of functions that tell us how to form new elements for this set.

Regarding the constructor:
- It's implicit that the only way for an element to be in the set is to be an basis element or to be made through a constructor.
- Example:
  - Basis: $0 \in E$
  - Constructor: If $e \in E$ then $- e \in E$ and $e + 2 \in E$ .
    - Resulting in two new elements:
    - $E = {0, - 0, 2}$
    - $E = {0, 2}$
  - If we continue, we can see that $E \subseteq Even Integers$ .