Chapter 9

In the beginning  Set: Collection of Objects  Examples: Arnold’s “set” of cars Arnold’s “set” of cars Nirzwan’s “set” of borrowed credit cards Nirzwan’s “set” of borrowed credit cards  Elements: those objects that are in a set Examples Examples The cars and the credit card #’sThe cars and the credit card #’s  Roster Method: when you write a set by enclosing the elements in braces A={1,2,3} A={1,2,3} Note: Typically, a set is designated by a capital letter Note: Typically, a set is designated by a capital letter ExampleExample B

After the beginning  Empty set (aka: null set)– Set with nothing in it Also uses { } sometimes Also uses { } sometimes Ex: The number of Mansions I ownEx: The number of Mansions I own X = { } X = { }  Union: (U) Shows a set that has the elements of 2 other sets.  What is A U B given A = {1,2,3,4} B = {3,4,5,6} A U B = {1,2,3,4,5,6} A U B = {1,2,3,4,5,6} Note: only list the elements that A and B have in common once! Note: only list the elements that A and B have in common once!

More of the beginning  Intersection What two or more sets have in common  Find A B given A = {1,2,3,4} B={3,4,5,6}  A B = {3,4}

Set Builder  Set Builder notation: another way to represent sets  2 parts to this 1. What you want to represent 1. What you want to represent Ex: all integers less than 8  x < 8Ex: all integers less than 8  x < 8 2. What numbers you can use 2. What numbers you can use Ex integers  x all integersEx integers  x all integers Other words that can be used instead of integersOther words that can be used instead of integers Positive or negative integers, real numbers, positive or negative real numbers, imaginary numbers! Positive or negative integers, real numbers, positive or negative real numbers, imaginary numbers!

Inequality  Ever see these before? These are symbols of inequality! These are symbols of inequality!  Examples are 4 > 2, 3x 87 and Nirzwan getting drug-searched outside of Burley!

Graphing an inequality in 1-D  Draw a number line appropriate for the problem  For less than or greater than use a parenthesis bracket, for less than or equal to or greater than or equal to, use a square bracket  Ex: x>1, x -3  Ex: x>5 U x 5 U x < 0

U Try Its  1 through 11?

Homework  Section 9.1 – 1-41 every other odd