RATIONAL AND REAL NUMBERS

Abstract

• What other properties do the Rational Numbers have that characterize them? Rational Order Is (Q,+,•) an ordered integral domain? Recall the definition of ordered. Ordered Integral Domain: Contains a subset D+ with the following properties. 1. If a, b ∈ D+ ,then a + b ∈ D+ (closure) 2. If a , b ∈ D+ , then a • b ∈ D+ (closure) 3. For each a ∈ Integral Domain D exactly one of these holds a = 0, a ∈ D+, -a ∈ D+ (Trichotomy)