# 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.

## Presentation on theme: "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."— Presentation transcript:

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.

Real Numbers

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

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 .

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

 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

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

Examples

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

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.

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

More Examples

Download ppt "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."

Similar presentations