Mathematical induction is a proof technique which applies to inductive sets, especially the set of non-negative integers. An induction proof on a set $$S$$ is carried out in two steps: in the induction basis, the claim is shown to hold for the minimal element in $$S$$; in the induction step, it is proven that, if the claim holds for a single but arbitrary $$k \in S$$ (the induction hypothesis), then it holds for the next element in $$S$$ ($$k+1$$ in case $$S = \mathbb{N}$$).