gen-in-3-4-sentences-explain-mathematical-induction-state-any-ke-3676

In 3-4 sentences, explain mathematical induction. State any key formula.

Mathematical induction is a proof technique used to establish that a statement P(n) is true for all natural numbers n ≥ n₀. It works in two steps: **(1) Base case** - prove P(n₀) is true, and **(2) Inductive step** - prove that if P(k) is true for some arbitrary k ≥ n₀, then P(k+1) must also be true. By these two steps, we can conclude P(n) holds for all n ≥ n₀, like dominos falling in sequence. **Key logical structure:** [P(n₀) ∧ ∀k(P(k) → P(k+1))] → ∀n≥n₀ P(n)