Number
,1.1 – Number Identification
Natural - whole numbers used when counting -- 1, 2, 3… - not 0
Integers - positive and negative numbers -- -2, -1, 0, 1, 2….
Whole - positive numbers - including 0
Irrational - A number that cannot be represented as a/b. They’re typically never ending
and don’t repeat. E.x. pi, √2.
Any square root containing a non-square number is irrational. E.x √5, √10
If you multiply/divide an irrational number by a rational one, it will still be irrational
Repeating decimals are typically not irrational numbers
Square number: A perfect square. Ex. 64, 16, etc.
,1.2 – Set theory
Set: Collection of well-defined objects, represented by uppercase letter
● Sets can be represented by Set Builder form
● Or Tabular Form, where each element is states
Subset: If all elements of set A IS IN SET b, THEN s IS SUBSET OF b
Proper subset: If all elements of set A is in B, but all elements of B is not in A, then it is called A
is a proper subset of B
Notation Meaning
n(A) Number of elements in set A
∈ Element of
Ex. 3 ∈ A means 3 is an element of set A
∉ Not an element of
Ex. 4 ∉ A means 4 is not an element of set A
, A’ Complement of set A (set of everything NOT in set A)
∅ Null/empty set
Universal set, the set with all members of every set.
/E
⊆|⊈ A is/is not a subset of B
⊂|⊄ A is/is not a proper subset of B
A∪B Union of A and B
A∩B Intersection of A and B, common elements of A and B
𝐴 ∪ 𝐵= A union B = Everything in A and B
𝐴 ∩ 𝐵= A intersection B = Everything in A and B
𝐴' 𝑜𝑟 AC = ___________ = Everything not in A = complement
A - B = What A has that B doesn’t = Taking elements of B away from A
1.5 – Fractions, decimals, percentages
Recurring decimals to a fraction
Recurring decimals: 0.77777
● Multiply the decimal by 100 or 10. E.x. .7777 x 10 = 7.777
● Subtract the original decimal to get that decimal multiplied by one less.
● E.x. 7.777 - 0.777 = 7 = 0.777 x 9
,1.1 – Number Identification
Natural - whole numbers used when counting -- 1, 2, 3… - not 0
Integers - positive and negative numbers -- -2, -1, 0, 1, 2….
Whole - positive numbers - including 0
Irrational - A number that cannot be represented as a/b. They’re typically never ending
and don’t repeat. E.x. pi, √2.
Any square root containing a non-square number is irrational. E.x √5, √10
If you multiply/divide an irrational number by a rational one, it will still be irrational
Repeating decimals are typically not irrational numbers
Square number: A perfect square. Ex. 64, 16, etc.
,1.2 – Set theory
Set: Collection of well-defined objects, represented by uppercase letter
● Sets can be represented by Set Builder form
● Or Tabular Form, where each element is states
Subset: If all elements of set A IS IN SET b, THEN s IS SUBSET OF b
Proper subset: If all elements of set A is in B, but all elements of B is not in A, then it is called A
is a proper subset of B
Notation Meaning
n(A) Number of elements in set A
∈ Element of
Ex. 3 ∈ A means 3 is an element of set A
∉ Not an element of
Ex. 4 ∉ A means 4 is not an element of set A
, A’ Complement of set A (set of everything NOT in set A)
∅ Null/empty set
Universal set, the set with all members of every set.
/E
⊆|⊈ A is/is not a subset of B
⊂|⊄ A is/is not a proper subset of B
A∪B Union of A and B
A∩B Intersection of A and B, common elements of A and B
𝐴 ∪ 𝐵= A union B = Everything in A and B
𝐴 ∩ 𝐵= A intersection B = Everything in A and B
𝐴' 𝑜𝑟 AC = ___________ = Everything not in A = complement
A - B = What A has that B doesn’t = Taking elements of B away from A
1.5 – Fractions, decimals, percentages
Recurring decimals to a fraction
Recurring decimals: 0.77777
● Multiply the decimal by 100 or 10. E.x. .7777 x 10 = 7.777
● Subtract the original decimal to get that decimal multiplied by one less.
● E.x. 7.777 - 0.777 = 7 = 0.777 x 9
