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.