Math 492/592
Homework 1.1 Number Sets
1. Fill-out the Number Set Definitions & Notation table; use our course definitions
(no paraphrasing)
NUMBER SET
NOTATION DEFINITION(S)
Counting Numbers
No symbol
used in
this course
Whole Numbers
W
Integers
Rational Numbers
Non-zero
Rational Numbers
Irrational Numbers
No symbol
used in
this course
Real Numbers
Non-zero
Real Numbers
Memorize the definitions of the number sets in the table (nothing to turn in).
Topic 1.1 Homework, page 1
2. For each part, give two examples of such numbers, or if two examples are not
possible, briefly explain why.
Example: An integer that is not a whole number: -1, -492
a. An integer that is a whole number
b. A whole number that is not a counting number
c. An integer that is a rational number
d. A fraction that is a rational number
e. A fraction that is not a rational number
f. A real number that is not a rational number
g. A real number that is a rational number
h. A square root that is a rational number
i. A square root that is not a rational number
j. A rational number that is not a real number
k. A fraction that is an integer
l. A fraction that is not an integer, but is a rational number
Topic 1.1 Homework, page 2
3. Prove each of the following using the definitions of the number sets. Use
appropriate notation.
a. Q  R
b.
3
is a rational number.
7
c. 4.929229222922229222229 . . . is not a rational number assuming the
pattern of 9’s and 2’s continues (a 9 is followed by one 2, then a 9 followed
by two 2’s, then a 9 followed by three 2’s, etc.).
d. -26.88865932 is a rational number.
Topic 1.1 Homework, page 3
4. The following is from a middle school math text book. (It shall remain nameless
to protect the guilty!) Example 2a is misleading when one compares it to the
given definition of “irrational number.” Why? (Hint – don’t forget to use your
own calculator to follow the given directions)
Topic 1.1 Homework, page 4