Set & Interval Notation

Sets and Elements A set is a collection of objects. To denote a set we often enclose a list of its elements with braces. This is called the Roster Method. Natural Numbers {1, 2, 3, 4, 5, …} Whole Numbers {0, 1, 2, 3, 4, …} Integers {…, -3, -2, -1, 0, 1, 2, 3, …} Since every natural number is also a whole number, we say that the set of natural numbers is a subset of the set of whole numbers.

Set Builder Notation A set can also be written in set builder notation. In this method, we write a rule that describes what elements are in a set. For example: {x | x is greater than 2.} The graph would look like either of the following: OR A rule that describes membership in the set The set of all x Such that

Example 1: Writing & Graphing Set Notation

Interval Notation Graphs of sets of real numbers are often portions of a number line called intervals. The interval can be written in interval notation. For example, for -2 < x ≤ 1 we write the interval notation as (-2, 1]. Parentheses are used to show it does not contain that number, where brackets show it does contain that value.

Example 2: Graph & Write in Interval Notation {x|x is less than 9.} {x|x is greater than or equal to 6.} {x|x is greater than or equal to -5 and less than or equal to 6.} {x|x is great than 2 and less than or equal to 8.}

OR Compound Inequalities and Union The graph of the set {x|x is less than -2 or greater than 3} is shown below. This graph is called the union of two intervals and can be written in interval notation as seen below. (-∞, -2) U (3, ∞)

Example 3: Unions {x|x is greater than 5 or less than 4.} {x|x is less than or equal or -1 or greater than 2.}