...
N = {1, 2, 3, 4, 5, 6, . . .}
6
W = {0, 1, 2, 3, 4, 5, . . .}
|a|
a
Z = {. . . , −3, −2, −1, 0, 1, 2, 3, . . .}
Q = { qp |p
−2
2
q ̸= 0}
q
0
I = {a|a
√
π = 3.1415927 . . .
R = {a|a
}
2 = 1.4142136 . . .
}
{2, 4, 6}
N, W, Z, Q, I
R
8
{x|x
1
{2, 4, 6}
5
6
7.}
0
√
−2, 0, 14 , −1.5, 112, −3, 11, 3
⎧
⎪
⎪
⎨
⎪
⎪
⎩
⎫
⎪
⎪
⎬
⎧
⎪
⎪
⎨
⎪
⎪
⎭
⎪
⎪
⎩
1
3 , 0, 1.5, −57, 3, 11,
N 112, 11
W 0, 112, 11
Z −2, 0, 112, −3, 11
Q −2, 0, 14 , −1.5, 112, −3, 11
√
I
3
√
R −2, 0, 14 , −1.5, 112, −3, 11, 3
5
6
5
6
|5|
5
|0|
0
|−4.2|
|−3|
(
(
(
(
(
(
(
(
4.2
(
(
(
(
(
(
(
(
(
2
3
(
(
(
(
(
(
(
(
3
√
− 3
(
(
(
(
(
(
(
(
(
√
3
7, −π
⎫
⎪
⎪
⎬
⎪
⎪
⎭
−2
2
3
√
− 5
N
W
Z
Q
I
−1.52
−4, 0, 2.5, 12 , 5
R
|−8|
|7|
−25
|0|
(
(
(
(
(
(
(
(
2
3
√
(
(
(
(
(
(
(
(
(
√
(
(
(
(
(
(
(
(
2
(
(
(
(
(
(
(
(
(
|−3.8|
|−4|
|5|
(
(
(
(
(
(
(
− 58
|−1.75|
(
(
(
(
(
(
(
√
− 7
(
(
(
(
(
(
(
(
(
(
(
(
(
(
|7.2|
a
0
2
0
Number Sets and Absolute Value
Answers to Practice
1. Tell which set or sets each number belongs to: N, W, Z, Q, I, and R.
(a) 8
N, W, Z, Q, R
(b) 0
W, Z, Q, R
(c) −2
(d)
2
3
√
(e) − 5
Z, Q, R
Q, R
I, R
(f) −1.52
Q, R
2. Plot each number in the list on the real number line. −4, 0, 2.5, 12 , 5
−4
0
−5 −4 −3 −2 −1
0
1
2
2.5
1
2
5
3
4
5
3. Find the absolute value of each number.
(a) |−4|
(c) − 5 8
√ (e) − 7
(b) |5|
4
(d) |−1.75|
5
8
√
7
(f) |7.2|
1
5
1.75
7.2