1.2 Field Axioms (Properties)

Notes on a Handout

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

MULTIPLICATION

Closure:

Commutative:

Associative:

Multiplicative Identity (1 is the identity):

Multiplicative Inverse:

Distributive Property: a(b + c) = ab + ac

a•b is a unique real number

ab = ba

(ab)c = a(bc)

a • 1 = a

who ‘associate’ with

flip order

11a

a

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

Example Answers

1) Multiplicative Identity

2) Commutative for Addition

3) Additive Inverse

4) Distributive