Proof — Peano axiom 5: Mathematical induction
Statement
If a property P holds for 0, and whenever P(n) holds then P(S(n)) holds, then P holds for all natural numbers.
Formula
(P(0) ∧ ∀n (P(n) ⇒ P(S(n)))) ⇒ ∀n P(n)
Source
G. Peano, Arithmetices principia, nova methodo exposita, 1889
Domains
mathematics