Is there a set whose power set is countably infinite?
42095
Existence in ZF of a set with countable power set
132537
Class of sets of a given infinite cardinality
12436
The cardinality of the set of all finite subsets of an infinite set
147136
Subset of a countable set is itself countable
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
52682
Is the power set of the natural numbers countable?
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
102113
Proof that the number of proofs is countably infinite
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
91237
Every infinite set contains a countable subset
47697
Russell's paradox: a set cannot contain its own powerset
66301
The cardinality of the set of countably infinite subsets of an infinite set
112910
Is the set of real numbers really uncountably infinite?
103769
The Cartesian product of a finite number of countable sets is countable
149673
Cardinality of an infinite union of finite sets
147920
Infinite powering by $i$
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$