Proof by Induction

Definitions

1. A proof technique that establishes a statement for all natural numbers by proving a base case and then showing that if the statement holds for n, it must hold for n+1. Structural induction generalizes this to recursive data structures like trees and lists.

   In plain English: Prove something works for the first case, then prove that if it works for any case it must work for the next one. Like dominoes — knock one over and they all fall.

   Example: "We proved the loop invariant holds by induction on the iteration count — base case is trivial, inductive step follows from the swap."

Related Terms

• Dynamic Programming
• Recurrence Relation
• Category Theory