Proving that set is either finite or countable
47637
Are strict local minima of a general function always countable?
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
153652
Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
149673
Cardinality of an infinite union of finite sets
66398
Union of a finite set and a countably infinite set is countably infinite
45792
Rigorous proof that surjectivity implies injectivity for finite sets
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
63276
Is an arbitrary union of a chain of countable sets countable?
154474
Image of countable and uncountable sets
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
68230
The cardinality of a countable union of sets with less than continuum cardinality
122506
Relation on countable sets
75019
Infinite Cartesian product of countable sets is uncountable
32774
Finite Cartesian Product of Countable sets is countable?
42095
Existence in ZF of a set with countable power set
147136
Subset of a countable set is itself countable
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality