## 5.6 Outline

- Definition of real numbers
- definition
- decimal representation
- terminating decimal
- repeating decimal
- change fractional form to decimal form
- change terminating decimal form to fractional form

- real number line
- unit distance
- number line
- dense set

- classifications within the set of real numbers

- Identity and inverse properties
- closure for addition and multiplication
- associative for addition and multiplication
- commutative for addition and multiplication
- distributive for multiplication over addition
- identity for addition; definition of zero
- identity for multiplication; definition of one
- inverse property for addition; definition of opposite
- inverse property for multiplication; definition of reciprocal

- Algebraic structure
- group
- commutative group
- Abelian group
- field

Here is a nice graphing showing the exact location of the irrational number pi:

## 5.6 Essential Ideas