# R-and-i-arithmetic

Recursion and Induction: Arithmetic

We will next discuss arithmetic, in two steps. First, we'll
challenge you to use what we have already got to define “natural
numbers” (non-negative integers) and the elementary operations on them. This
is called “Peano” arithmetic after the 19th century Italian
mathematician Giuseppe Peano who first wrote down formal axioms describing
the natural numbers.

After you've explored the foundations of arithmetic, we'll talk about
briefly about the more familiar arithmetic of integers and rationals.

Next: Peano
Arithmetic (or Table of Contents)

### Subtopics

- R-and-i-ACL2-arithmetic
- Recursion and Induction: ACL2 Arithmetic
- R-and-i-peano-arithmetic
- Recursion and Induction: Peano Arithmetic