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Published byNoel Kelley Modified over 8 years ago

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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.

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Real Numbers

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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

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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 .

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

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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

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

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Examples

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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

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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.

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

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More Examples

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