The infinite domino

Observation — The infinite domino

Think of an infinite row of domino tiles: the base says “the first one falls”; the inductive step says “if the $k$-th one falls, it makes the next one fall too”. Hence they all fall.

Induction is the formalisation of this intuition, and it is valid precisely because the naturals are well-founded (every non-empty subset has a minimum). The domino metaphor as the “transport” of the truth value from $P(k)$ to $P(k+1)$ is discussed by Esty (ch. 5) as a linguistic reinterpretation of the conditional “for every $k$, if… then…”.

Links

Topics: Set theory
Concepts: Principle of induction
Methods: Induction