Show that the family of sets is countable
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
42794
Prove that functions map countable sets to countable sets
18223
Prove that the union of two disjoint countable sets is countable
70143
Mutually exclusive countable subsets of a countable set
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
130361
Basis for a topology with a countable number of sets
128118
Is the cofinite topology on a countable set first countable?
75019
Infinite Cartesian product of countable sets is uncountable
81509
The cardinality of a countable union of countable sets, without the axiom of choice
136321
Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
44623
Closed set as a countable intersection of open sets
110635
Proving $\mathbb{N}^k$ 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
102113
Proof that the number of proofs is countably infinite
10702
Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
99599
Uncountable and countable