Download Sets and Whole- Number Operations and Properties

What is a set?
Sets and WholeNumber Operations
and Properties
Section 2.1
Sets and Whole Numbers
Types of Sets
A set with no elements is called the _________,
or null set, and is denoted by { } or Ø.
n( { } ) = n(Ø) = 0
Example: The set of all whales that are not
mammals.
„ A set with a limited number is called a _______
_________.
Example: The set of people in this classroom.
„ A set with an _________ number is called an
infinite set.
Example: The set of whole numbers.
„
Sets A and B are _________ _________,
A=B, if and only if each element of A is
also an element of B and each element of
B is also an element of A. (Must have
exactly the same elements.) n(A) = n(B)
Example: T = {t,e,a,c,h,e,r} and
C = {c,h,e,a,t,e,r}
T=C
A set is any _________ of objects or ideas
that can be listed or described.
„
Example: The set of whole numbers
W = { 0, 1, 2, 3, 4, 5, …}
„
Each individual object in a set is called an
_________ of the set.
One-to-One Correspondence
„
Equal Sets
„
„
Sets A and B have a __________________
correspondence if and only if 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.
Example: Individuals and Social Security
Numbers
Equivalent Sets
Sets A and B are _________ _________,
A~B, if and only if there is a one-to-one
correspondence between A and B.
„ same or different types of elements
„ n(A) = n(B)
Example: U = {red, white, blue} and
S = {1, 2, 3}
U~S
„
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Whole Numbers and Sets
„
„
Subsets
A _________ _________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).
When _________ two whole numbers,, you
y can
look at sets for each of the numbers. If a one-toone correspondence cannot be made between
the elements of two sets, the set with elements
left over is said to have more elements than the
other set and the whole number for that set is
greater than that of the other set.
Greater than >
Less than <
Two Types of Subsets
For all sets A and B, A is a _________ of
B, symbolized as A ⊆ B, if and only if each
element of A is also an element of B.
„ Example:
U = {square, circle, rectangle, triangle}
A = {circle, triangle, rectangle}
proper subset
B = {triangle, square, rectangle, circle}
improper subset
„
Determining the Number of Subsets
„
{1}
{1,2}
c) {1,2,3}
d) {1,2,3,4}
… Write a rule for the number of subsets with n
elements.
a)
A _________ subset identifies a subset
that contains part, but not all, of the
elements of a set. If X is a subset of Z,,
then Z contains more elements than X.
„ An _________ subset is a subset that
contains all the elements of the set. If X is
a subset of Z, then X is equal to Z.
„
b)
… Write
a rule for the number of proper subsets with n
elements.
Number Sets (continued)
Number Sets
„
„
„
Whole Numbers: the individual whole numbers,
including _________, that comprise a single set
of infinite numbers.
W = { 0, 1, 2, 3,…}
Natural (Counting) Numbers: the infinite set of
whole numbers, excluding zero, that is used in
_________.
N = {1, 2, 3, 4, …}
Integers: the infinite set of _________ whole
numbers, negative numbers, and zero.
I = {…, -3, -2, -1, 0, 1, 2, 3, …}
List all subsets of:
„
_________ Numbers: the infinite set of positive and
negative numbers that can be described as a
comparison of two integers. (Fractions, repeating
decimals, terminating decimals)
Q = {…, -1, -¾, -.15, 0, ¼, ½, ⅞, 1, …}
„
_________ Numbers: the infinite set of positive and
negative numbers that cannot be expressed as a
comparison between two numbers.
(non-repeating, non-terminating)
„
_________ Numbers: the infinite set of numbers that
include the rational numbers and the irrational
numbers.
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Real Numbers
Irrational
Numbers
Rational Numbers
Integers
Whole
Numbers
Natural
(Counting)
Numbers
Classroom Activity
„
„ ROLEPLAY!
Using a set of nesting boxes, have student
volunteers come to the front of the room
and illustrate the REAL NUMBER
SYSTEM.
Activity Materials
„ 6 boxes: 4 that will stack inside each
other, a 5th that when put with 4 nested will
all fit inside largest,
g , 6th box
„ Label each box with the appropriate name.
(Real Numbers, Irrational Numbers, Rational
Numbers, Integers, Whole Numbers,
Natural Numbers)
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