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Introduction to Set Builder Notation

Introduction to Set Builder Notation. By: R.Prevost. Contents. What is a set? How to write sets Set-builder notation. What is a set?. A set is a collection of objects which can be listed These object in the collection are called elements. How to write sets.

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Introduction to Set Builder Notation

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  1. Introduction to Set Builder Notation By: R.Prevost

  2. Contents • What is a set? • How to write sets • Set-builder notation

  3. What is a set? • A set is a collection of objects which can be listed • These object in the collection are called elements

  4. How to write sets • Conventionally, the pair of set braces, { } , are used to enclose the elements of a set, using commas to separate the individual elements. • Capital letters are normally used as names for sets. • If an object x is an element of set A, it is denoted by x Î A. • x Ï A means x is not an element of A

  5. Writing sets continued • The union of two sets A and B, denoted as A È B, is the set of all elements that are contained in sets A, B or both. • The intersection of two sets A and B, denoted as A Ç B, is the set of all elements that belong to both sets A and B. • An empty set has no elements; it is also called the null set and is denoted as Æ.

  6. Set-builder Notation • Set-builder notation is generally used to represent a group of real numbers • It stipulates that sets be written in the format { x : x has property Y } , which is read as "the set of all elements x such that x has the property Y."

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