MMW Flashcards
The first person who introduced the Fibonacci Sequence
Leonardo of Pisa (also known as Fibonacci)
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…
Fibonacci Sequence
the oldest known recursive sequence, which is a sequence where each successive term can only be found through performing operations on previous terms.
Fibonacci Sequence
The Value of the Golden Ratio
positive negative 1.61803
What Greek Letter represents the Golden Ratio
Greek Letter Phi
Other names of Golden Ratio
Golden Mean, Golden Section
Any Group or collection of objects is called a ________
Set
The objects than belong in a set
Elements or Members
A way of expressing sets by putting the elements of the set inside a pair of braces, { }
ROSTER METHOD
Change into Roster Method:
- The set of denominations of U.S. paper
currency in production at this time
{$1, $2, $5, $10, $20, $50, $100}
Change into Roster Method:
- The set of states in the United States
that border the Pacific Ocean
{California, Oregon, Washington, Alaska, Hawaii}
Use the roster method to represent the set of the days in a week.
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
What are the Natural Numbers or Counting Numbers
N= {1, 2, 3, 4, 5, …}
What are the Whole Numbers
W= {0,1,2,3,4,5,…}
What are the Integers
Z= {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …}
What are the Rational Numbers
Q= the set of all terminating or repeating decimals
What are the Irrational Numbers
J= the set of all non-terminating, nonrepeating decimals
What are the Real Numbers
R= the set of all rational or irrational numbers
Natural numbers is also known as?
Counting Numbers
The three dots in a set is called a/an?
Ellipsis
The set of natural numbers less than 5
{1, 2, 3, 4}
The solution set of x + 5= -1
{-6}
A set is ___________ if it is possible to determine whether any given item is an element of the set.
WELL DEFINED
The set that contains no elements
Empty set or Null set
Another method of representing a set, especially useful when describing infinite sets.
Set-Builder Notation
The Set is __________ if the number of elements in the set is a whole number.
FINITE
The number of elements in the set
Cardinal Number of a Finite Set
Set A is _________ to Set B, if and only if A and B have exactly the same elements regardless of order
EQUAL
Set A is _________ to Set B, if and only if A and B have the same number of elements regardless of order
EQUIVALENT
The set of all elements that are being considered
Universal Set
Denoted with S(‘), is the set of all elements in the universal set U that are not elements of A
Complementary Set
Set A is a/an ________ of Set B, if and only if every element of A is also an element of B
SUBSET
Is an empty set a subset of every set?
Yes
Set A is a/ an __________ of set B, if every element of A is an element of B, and A is not equal to B
PROPER SUBSET
Is this a proper subset?
R= {Mars, Venus} and S= {Mars, Venus, Mercury}
YEs
Is this a proper subset?
T= P{Europe, Africa} and V= {Africa, Europe}
No
A set with n elements has 2^n subsets
Number of Subsets
It is the set of elements common to both A and B
INTERSECTION of sets
Is the set that contains all the elements that belong to A or to B or to both
UNION of sets
The regions obtained by joining the
regions represented by A (i, ii) and the
regions represented by B (i, iii)
Answer in its Set form
A Union B
The region in U that is not in (A U B)
The complement of A Union B
“the complement of the intersection of two sets is the union of the complements of the sets.”
De Morgan’s Law
