Download File

Welcome to
Mathematics!
{
YAY ALGEBRA!
A set is a collection of objects
 Each object in a set is called an element
 A set with no elements is called the null set or
empty set
 Infinite set has an infinite number of elements
 A set with a finite or limited number of elements is
a finite set
 A subset is a set within a set

Vocabulary you need to
know!
What is an example of an infinite set?
 What is an example of a finite set?
 What is an example of an empty set?

Examples of sets






Natural Numbers: the numbers used to count objects or things
Whole numbers: the set of natural numbers and zero
Integers: the set of whole numbers and the opposites of the natural
numbers
Rational numbers: numbers that can be written in the form a/b, where a
and b are integers and b ≠ 0. In decimal form, they can repeat of
terminate
Irrational numbers: numbers that cannot be written as the quotient of
two integers; in decimal form, irrational numbers do not repeat or
terminate
Real Numbers: the set including all rational and irrational numbers
Subsets of Real Numbers
For each number, identify the subset of real numbers to
which it belongs:
½
{rational numbers, real numbers}
5
{natural numbers, whole numbers, integers, rational
numbers, real numbers}
3√2
{irrational numbers, real numbers}
Examples!
Identify the set of numbers that best describes the situation
(explain your reasoning)
The value of bills in a person’s wallet
Whole numbers… empty set?
The balance of a checking account
Rational... Could be positive or negative and have decimals
The circumference of a circular table when the diameter is a
rational number
Irrational... Why?
More Examples: Word
Problems
The union of two sets is
everything in both sets
 The symbol for the Union of two
sets is a capital “∪”
 For example, if you have the set
{1, 2, 3, 4, 5} and the set {2, 4, 6},
the Union (∪) of the two sets is {1,
2, 3, 4, 5, 6}
 Venn Diagram Example:

Union
An element is written just one time even if it
exists in both of the sets
 Union of the two sets is commutative
 If A and B are two sets, then A ∪ B = B ∪ A
 Union of sets is also associative
 If A, B and C are three sets, then A ∪ (B ∪ C)
= (A ∪ B) ∪ C

Union Continued
The intersection of sets is noted by the
symbol ∩
 Defined as the grouping up of the
common elements of two or more sets
 For example, given Set A = {1, 2, 3, 7,
11, 13} and Set B = {1, 4, 7, 10, 13, 17};
A ∩ B = {1, 7, 13}

Intersection
Intersection of sets is an associative operation for
three sets
 Given sets A, B and C… A ∩ (B ∩ C) = (A ∩ B) ∩ C
 What if there are no elements in common!?!?!
 Denoted by the Empty Set or ∅
 Example: Given set A = {1, 3, 5} and set B = {2, 4, 6}
A∩ B = ∅

Intersection Continued

A closed set is one where under a given operation if
the outcome of the operation on any two members of
the set is also a member of the set.
Determine if the statement is True or False: Provide a
counterexample if False
 The set of whole numbers is closed under addition…
 The set of whole numbers is closed under
subtraction

Identifying A Closed Set