Peano Axioms

definitionreal-analysisnatural-numbers

Definition

The set of natural numbers is the set described by the following:

• $1\in \mathbb{N}$.
• If $n\in \mathbb{N}$, then $n+1\in \mathbb{N}$.
• “Induction”: if $S\subset \mathbb{N}$ is a subset so that
  • $1\in S$
  • If $n\in S$, then $n+1\in S$ Then $S=N$.

Examples