## 2.4. The Real Number System

### Theorem 2.4.6: Properties of R and Q

- The set of real numbers satisfies the
**Archimedean Property**: - Let
*a*and*b*be positive real numbers. Then there is a natural number*n*such that*n * a > b* - The set of rational numbers satisfies the following
**Density Property**: - Let
*c < d*be real numbers. Then there is a rational number*q*with*c < q < d*.