1. Real Number System You will be able to represent subsets of the real number system using set-builder and interval notation. HW: Set and Interval Notation Worksheet; Watch review videos to help.

2. Real Numbers

3. Terms  A set is a collection or list of things, typically numbers. Abbrev: {1, 4, 7, 9}  A subset is a smaller set within the set.  The empty set { } is abbreviated by ø

4. Examples  = set of integers: {…, -2, -1, 0, 1, 2, …}   = set of rational numbers   = set of natural numbers {1, 2, 3, 4, …} , , and  area all subsets of .

5. Real Numbers,  Rational Numbers,  Noninteger Signed Fractions Integers, Whole Numbers 0 Natural Numbers,  Negative Natural Numbers Irrational Numbers

6.  We can represent  by the number line:  Subsets can be represented by intervals.  Ways to express intervals: 1. Inequalities 2. Set-Builder Notation 3. Interval Notation

7. Set-Builder Notation PhraseSymbol Less than< Less than or equal to< Greater than> Greater than or equal to> Such that|, : Element of 

8. Examples

9. Interval Notation Terms: PhraseSymbol Positive infinity; Increasing without bound  Negative infinity; Decreasing without bound-- Lower bound, inclusive[ Lower bound, exclusive( Upper bound, inclusive] Upper bound, exclusive) UnionU

10. Interval Notation (more ideas…)  Because +/-  is not a number, its bound is always excluded: ( or ).  Intervals that start with [ and end with ] are closed.  Intervals that start with ( and end with ) are open.

11. Examples GraphSet-BuilderInterval Notation Interval Type 1. 2. 3. 4. 5. 6. 7.Open 8.Closed

12. More Examples