Can the reals be the union of a countable set and a set of lower cardinality?
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
15438
do all uncountable sets have same cardinality as real numbers?
63276
Is an arbitrary union of a chain of countable sets countable?
136006
Prove that any countable cartesian product of countable sets is countable
94825
Open set as a finite union of closed sets
68994
Countable closed sets
88904
Help with a proof. Countable sets.
44974
Infinite set and countable subsets
14972
Cardinality of Vitali sets: countably or uncountably infinite?
1396
cardinality of all real sequences
13620
$\omega_2$ is a not countable union of countable sets without AC
35043
Cardinality of a set A is strictly less than the cardinality of the power set of A
87830
Relating the union of the power set of a set to the set itself
12436
The cardinality of the set of all finite subsets of an infinite set
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
82628
Cardinality of a set of closed intervals
152976
Real Analysis: open and closed sets