Test 1 - Math 136
Natural Numbers
N = (1, 2, 3, 4, 5...)
Whole Numbers
W = (0, 1, 2, 3, 4, 5...)
Integers
I = (-4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational and Irrational Numbers
Q = Repeating Decimals
J = Non-repeating Decimals
Real Numbers
Rational and Irrational numbers
Well Defined Set
Possible to determine all the numbers in the set.
Ex. The alphabet
∈
"Is an element of"
Ex. 4 ∈ N: 4 is an element of the set of natural numbers.
∅ or ( )
Empty set symbol
Ex. Consider the set of natural numbers that are negative. = ∅
Set Builder Notation
A description with algebra:
( x | x ∈ N and x > 7)
The set of all elements of X such that X is an element of the set of natural numbers and X is
greater than 7.
, Cardinal Numbers
The number of elements in a given set.
Equal/Equivalent Sets
·Equal Sets have the exact same elements.
·Equivalent Sets have the same number of elements.
Universal Set
The set of all elements that are being considered.
The Complement of a Set
Complement = NOT
·The complement of Set A, denoted by A', is the set of all elements of the universal set U
that are not elements of A.
EX:
U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
S = (2, 4, 6, 7)
T = (x | x < 10 and x ∈ the odd numbers)
S' = (1, 3, 5, 8, 9, 10)
T' = (2, 4, 6, 8, 10)
A Subset of a Set
·Set A is a subset of set B, denoted by A ⊆ B, if and only if every element of A is also an
element of B.
Subset Relationships
A ⊆ A for any set A
∅ ⊆ A for any set A
Every set is a subset of itself
Natural Numbers
N = (1, 2, 3, 4, 5...)
Whole Numbers
W = (0, 1, 2, 3, 4, 5...)
Integers
I = (-4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational and Irrational Numbers
Q = Repeating Decimals
J = Non-repeating Decimals
Real Numbers
Rational and Irrational numbers
Well Defined Set
Possible to determine all the numbers in the set.
Ex. The alphabet
∈
"Is an element of"
Ex. 4 ∈ N: 4 is an element of the set of natural numbers.
∅ or ( )
Empty set symbol
Ex. Consider the set of natural numbers that are negative. = ∅
Set Builder Notation
A description with algebra:
( x | x ∈ N and x > 7)
The set of all elements of X such that X is an element of the set of natural numbers and X is
greater than 7.
, Cardinal Numbers
The number of elements in a given set.
Equal/Equivalent Sets
·Equal Sets have the exact same elements.
·Equivalent Sets have the same number of elements.
Universal Set
The set of all elements that are being considered.
The Complement of a Set
Complement = NOT
·The complement of Set A, denoted by A', is the set of all elements of the universal set U
that are not elements of A.
EX:
U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
S = (2, 4, 6, 7)
T = (x | x < 10 and x ∈ the odd numbers)
S' = (1, 3, 5, 8, 9, 10)
T' = (2, 4, 6, 8, 10)
A Subset of a Set
·Set A is a subset of set B, denoted by A ⊆ B, if and only if every element of A is also an
element of B.
Subset Relationships
A ⊆ A for any set A
∅ ⊆ A for any set A
Every set is a subset of itself
