Let $X$ be a countable set. Then which of the following are true?
92005
Existence of compact/complete metric on countable set
152563
Set of discontinuity of monotone function is countable
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
23907
$Seq (\mathbb{N})$ of all finite sequences of elements of $\mathbb{N}$ is countable.
11959
What's wrong with this argument that $[0,1]$ is countable?
10513
What is the significance of the term "separable" in the context of countability properties?
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
68230
The cardinality of a countable union of sets with less than continuum cardinality
41192
Neatest proof that set of finite subsets is countable?
70143
Mutually exclusive countable subsets of a countable set
76240
How is $\epsilon_0$ countable?
80096
Prove that the union of countably many countable sets is countable.
44623
Closed set as a countable intersection of open sets
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
19297
Is the cofinite topology on an uncountable set first countable?
35692
The set of all finite subsets of the natural numbers is countable