Set of Real Numbers
Set of Real Numbers
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



Set – a collection of objects
Real Numbers – Include both rational and
irrational numbers
Natural Numbers – Numbers used for
counting (1,2,3,…)
Whole Numbers – natural numbers with 0
included (0,1,2,3,…)
Integers – Set of whole numbers and
their opposites (…,-4,-3,-2,1,0,1,2,3,4,…)
Sets
x x is a natural number less than 3
The set of
such that
All number x
x is a natural number less than 3
Elements in a set
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
The members of a set are called its
elements.
A set that contains no elements is
called the empty set (or null set)
symbolized by  or  
The set
x x is a month with 32 daysis  or  
Rational and Irrational Numbers
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Rational Numbers can be expressed
as an integer divided by a nonzero
integer
Irrational Numbers are numbers
whose decimal representation
neither terminates nor has a
repeating block of digits. They
cannot be represented as the
quotient of two integers.
Examples of Rational Numbers

4

8.734,
-5, 0, 9.45,

7
Examples of Irrational Numbers

 10, 3,  , 7.161161116..., 3.491...
Given the following numbers…
1.
2.
3.
4.
5.
6.
Name
Name
Name
Name
Name
Name
20,  10,  5.34, 18.999,
11
, 7,  2,
45
2
0,  , 9.34334333433334...
3
the
the
the
the
the
the
natural numbers
whole numbers
integers
irrational numbers
rational numbers
real numbers
True or False?
a.
b.
c.
d.
3 is a real number
1 is an irrational number
5
Every rational number is an integer

is a real number
Subsets

Subsets – sets contained within

Ex: Every integer is also a rational
number. In other words, all the
elements of the set of integers are also
elements of the set of rational
numbers. When this happens we say
that the set of integers, set Z, is a
subset of the set of rational numbers,
set Q. In symbols,
Z Q
Symbols
 used to denote that an element is in a particular set
is read as is not an element of
3  1, 2,3, 4,5
3 is an element of
{1,2,3,4,5}
p  a,5, g , j, q
p is not an element of
{a, 5, g, j, q}
List the elements in each set.
x
x is a whole number between 1 and 6
x
x is a rational number greater than 100
Practice
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