Download Sets and Whole-Number Operations and Properties

What is a set?
Sets and Whole-Number Operations
and Properties
Section 2.1
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Sets and Whole Numbers
y A set is any __________ of objects or ideas that can be listed or
described.
y Example: The set of whole numbers
W = { 0, 1, 2, 3, 4, 5, …}
y Each individual object in a set is called an ________ of the set.
Types of Sets
y 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.
y A set with a limited number is called a ____________.
Example:
p The set of ppeople
p in this classroom.
y A set with an ___________ number is called an infinite set.
Example: The set of whole numbers.
Equal Sets
y 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} and
C = {c,h,e,a,t}
{c h e a t}
T=C
One-to-One Correspondence
y 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
y Sets A and B are ___________, A~B, if and only if there is a
one-to-one correspondence between A and B.
y same or different types of elements
y n(A) = n(B)
Example: U = {red, white, blue} and
S = {1
{1, 22, 3}
U~S
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Whole Numbers and Sets
y 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).
y When _____________ two whole numbers, you can look
at sets for each of the numbers. If a one-to-one
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
y 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.
y 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.
Subsets
y 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.
y Example:
U = {square, circle, rectangle, triangle}
A = {{circle,
i l triangle,
i l rectangle}
l }
proper subset
B = {triangle, square, rectangle, circle}
improper subset
Determining the Number of Subsets
y List all subsets of:
{1}
{1,2}
c) {1,2,3}
d) {1,2,3,4}
y Write a rule for the number of subsets with n elements.
a)
b)
y Write a rule for the number of proper subsets with n elements.
Number Sets
y Whole Numbers: the individual whole numbers, including
_________, that comprise a single set of infinite numbers.
W = { 0, 1, 2, 3,…}
y Natural (Counting) Numbers: the infinite set of whole
numbers excluding zero
numbers,
zero, that is used in _________.
N = {1, 2, 3, 4, …}
y Integers: the infinite set of __________ whole numbers,
negative numbers, and zero.
I = {…, -3, -2, -1, 0, 1, 2, 3, …}
Number Sets (continued)
y __________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, …}
y __________Numbers: the infinite set of p
positive and negative
g
numbers that cannot be expressed as a comparison between two
numbers.
(non-repeating, non-terminating)
y __________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
Classroom Activity
y ROLEPLAY!
y Using a set of nesting boxes, have student volunteers come to
Integers
Whole
Numbers
the front of the room and illustrate the REAL NUMBER
SYSTEM.
Natural
(Counting)
Numbers
Activity Materials
“Math is a Wonderful Thing”
y 6 boxes: 4 that will stack inside each other, a 5th that when
put with 4 nested will all fit inside largest, 6th box
y Label each box with the appropriate name.
(Real Numbers, Irrational Numbers, Rational Numbers,
Integers Whole Numbers
Integers,
Numbers, Natural Numbers)
y http://www.youtube.com/watch?v=jXx04EiMbS0
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