👉 Pe math, or Peano arithmetic, is a formal system for axiomatizing the natural numbers, designed to rigorously define arithmetic operations and properties like addition and multiplication without relying on intuitive notions. It starts with a set of axioms: a zero element (0), a successor function (S(n) = n + 1) that generates all natural numbers, and axioms for induction (principle of mathematical induction). These axioms systematically build the natural numbers from 0, defining operations recursively and ensuring consistency. Peano arithmetic avoids paradoxes like Russell’s by carefully structuring its syntax, making it foundational for formal logic, computer science, and mathematical foundations. Its simplicity and precision allow it to model basic arithmetic while highlighting the limits of formal systems, as seen in Gödel’s incompleteness theorems.
