## 1.4. Natural Numbers, Integers, and Rational Numbers

### Definition 1.4.1: Peano Axioms

- 1 is a natural number
- For every natural number
*x*there exists another natural number*x’*called the successor of*x*. *1 # x’*for every natural number*x*(*x’*being the successor of*x*)- If
*x’ = y’*then*x = y* - If
**Q**is a property such that:- 1 has the property
**Q** - if
*x*has property**Q**then*x’*has property**Q**

- 1 has the property
- then the property
**Q**holds for all natural numbers.