Every time that a human being succeeds in making an effort of attention with the sole idea of increasing [their] grasp of truth, [they acquire] a greater aptitude for grasping it, even if [their] effort produces no visible fruit.
―Simone Weil, philosopher & political activist
In this chapter, we introduce mathematical induction, which is a proof technique that is useful for proving statements of the form \((\forall n \in \mathbb{N})P(n)\text{,}\) or more generally \((\forall n \in \mathbb{Z})(n\geq a\implies P(n))\text{,}\) where \(P(n)\) is some predicate and \(a \in \mathbb{Z}\text{.}\)
