If a countable union of sets has card $\mathfrak{c}$, prove at least one of them has card $\mathfrak{c}$
68230
The cardinality of a countable union of sets with less than continuum cardinality
70143
Mutually exclusive countable subsets of a countable set
27899
Can we prove the existence of $A\cup B$ without the union axiom?
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
87830
Relating the union of the power set of a set to the set itself
75019
Infinite Cartesian product of countable sets is uncountable
157513
How can I prove that these sets are countable infinite?
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
99478
countably infinite union of countably infinite sets is 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
111032
Proof of Sets involving the Cartesian Product
83518
Proving Two sets have same cardinality
139247
Real Analysis - Prove a set is countable
132868
Bijection between an infinite set and its union of a countably infinite set
78290
Countable axiom of choice: why you can't prove it from just ZF
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$