Transcript 2.1 Sets and Whole Numbers - Valdosta State University

2.1 Sets and Whole Numbers
Remember to Silence Your
Cell Phone and Put It In Your
Bag!
Sets
Intuitive definition of Set – A collection of
objects
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List the objects of a set within braces { }
When listing the objects of a set, separate them
with commas
Use a capital letter to name a set
Order of the elements is not important
Element x  A, x  A
A versus a
One-to-One Correspondence
Sets A and B have one-to-one
correspondence iff each element of A
can be paired with exactly one element
of B and each element of B can be
paired with exactly one element of A.
Equal and Equivalent Sets
Sets A and B are equal sets, symbolized by
A = B, iff each element of A is also an
element of B and each element of B is also an
element of A.
Sets A and B are equivalent sets,
symbolized by A  B, iff there is a one-to-one
correspondence between A and B.
Subset and Proper Subset
For all sets A and B, A is a subset of B,
symbolized as A  B, iff each element of A is
also an element of B.
For all sets A and B, A is a proper subset of
B, symbolized by A  B, iff A is a subset of B
and there is at least one element of B that is
not an element of A.
Additional Terminology
The Universal Set U
Empty Set or Null Set
Finite Set
Infinite Set
 { }
The Complement of a Set
The complement of set A, written Ᾱ,
consists of all of the elements in U that
are not in A.
Whole Number
A whole number is the unique
characteristic embodied in each finite
set and all the sets equivalent to it.
The number of elements in set A is
expressed as n(A) and is called the
cardinality of set A.
Counting
Counting is the process that enables
people systematically to associate a
whole number with a set of objects.
Ordering Whole Numbers
For whole numbers a and b and sets A
and B, where n(A) = a and n(B) = b, a
is less than b, symbolized as a < b, iff
A is equivalent to a proper subset of B.
a is greater than b, written a > b, iff
b<a
Special Subsets of the Set of
Whole Numbers
Counting Numbers or Natural Numbers
{1, 2, 3, 4, . . . }
Whole Numbers
{0, 1, 2, 3, . . . }
Even Whole Numbers
{0, 2, 4, 6, . . . }
Odd Whole Numbers
{1, 3, 5, 7, . . . }
Three Types of Numbers
Nominal Number
Ordinal Number
Cardinal Number
An announcer says:
"The student with ID number
50768-973 has just won second prize-four tickets to the big game this
Saturday."