1. 1.2 Field Axioms (Properties) Notes on a Handout

2. Look at whiteboard for examples! ADDITION Closure: Commutative: Associative: Additive Identity (0 is the identity): Additive Inverse: a + b is a unique real number a + b = b + a (a + b) + c = a + (b + c) a + 0 = a a + (–a) = 0 who ‘associate’ with flip order

3. MULTIPLICATION Closure: Commutative: Associative: Multiplicative Identity (1 is the identity): Multiplicative Inverse: Distributive Property: a(b + c) = ab + ac ab is a unique real number ab = ba (ab)c = a(bc) a 1 = a who ‘associate’ with flip order

4. EQUALITY OF REAL NUMBERS Reflexive Property: Symmetric Property: Transitive Property: Addition Property: Multiplication Property: a = a If a = b, then b = a If a = b & b = c, then a = c If a = b, then a + c = b + c ‘reflection’ in mirror If a = b, then ac = bc

5. Example Answers 1) Multiplicative Identity 2) Commutative for Addition 3) Additive Inverse 4) Distributive