Also called "reduction formula".In the proof theory, the inductive axiom is an axiom of Piano's arithmetic system, which can be written as:
F（a）， —→a，F（a'）
F（o）， —→a，F（s）
Where a 'is the successor of a, a does not appear in F (o) or a, and s is the attention item.
F (a) is called inductive formula.Mathematical induction is a special case of inductive axiom, which can be expressed as P (o) D (P (s) → P (s+1)) → C X P (x).It is often used to prove the nature of natural numbers.The inductive axiom means that if we can prove that there is F property for the natural number o, and any number a can deduce the subsequent F property, then there is F property for any term.
