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Sec. 1.1
Sets of Numbers
A set ___________________________________________________________________
A subset ________________________________________________________________
The empty set, ___________________________________________________________
Rational numbers ______________________________________________________,
where the denominator is not zero. The decimal form either terminates or repeats.
Irrational numbers _______________________________________________________,
and their decimal form do not terminate or repeat.
Ex. 1 Ordering and Classifying Real Numbers
A.
Consider the numbers 0.6, 2, 0, -5/2, and 0.5129. Order the numbers from least
to greatest
B.
Consider the numbers 0.6, 2, 0, -5/2, and 0.5129. Classify each number by the
subsets of the real numbers to which it belongs.
There are many ways to represent sets. You can use words or _____________________
in which the elements of a set are listed between braces { }.
Words
____________________________________________________
Roster Notation
____________________________________________________
A set can be finite like the set of billiard ball numbers or infinite like natural numbers
{1, 2, 3, 4, …}
A finite set __________________________________________________________
An infinite set ________________________________________________________
Many infinite sets, such as the ________________________, cannot be represented in
roster notation. Instead, you can use a _______________________.
The set of real numbers between 3 and 5, which is also an infinite set, can be represented
on a number line or by an inequality.
3<x<5
An _________________ is the set of all numbers between two endpoints, such as 3 and 5.
In interval notation the symbols ________________are used to include an endpoint in an
interval, and the symbols ____________are used to exclude an endpoint from an interval.
(3, 5) the set of real numbers between but not including 3 and 5.
An interval that extends forever in the positive direction goes to infinity _________and an
interval that extends forever in the negative direction goes to negative infinity _________.
Because positive and negative infinity are not numbers, they cannot be included in a set of
numbers, so ___________________ are used to enclose them in an interval.
Methods of Representing Intervals
Numbers less than 3
# line:
Inequality:
Interval Notation:
Numbers greater than or equal to -2
# line:
Inequality:
Interval Notation:
Numbers between 2 and 4
# line:
Inequality:
Interval Notation:
Number 1 through 3
# line:
Inequality:
Interval Notation:
Ex. 2 Interval Notation
Use interval notation to represent each set of numbers.
A.
4<x<6
B.
Another way to represent sets is __________________________________.
Set-builder notation _______________________________________________________.
Ex. 3 Translating Between Methods of Set Notation
Rewrite each set in the indicated notation.
A.
B.
C.