Reading Quiz Section 8.2
1. A set A is uncountable if and only if .
(a) There is a bijection between A and [0, 1].
(b) There is a surjection from R onto A.
(c) There is an injection from N into A.
(d) There exists no injection from A into N.
2. Which of the following sets are uncountable. Select all that apply.
(a) ( 1, 2] ∪{3 }
(b) N ×[1, 2]
(c) R \
1
n
: n ∈ N
(d) Q ∩[1, 2]
3. True or False: there is no set A such that there is a surjection from P(A) onto A.
Practice Problems Section 8.2
1. Describe explicit injections f : (0, 1) → B and g : B → (0, 1) where
B = [1, 2) ∪ {π} ∪ (4
√
2, 497]
Now explain why
|
B
|
= c.
