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 Open 8.Closed
More Examples