Prove "Infinite Sets Contain Countably Infinite Subsets" without Using Axiom of Choice.
119624
A Dedekind infinite set has a countably infinite proper subset
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
44974
Infinite set and countable subsets
139247
Real Analysis - Prove a set is countable
82009
Prove that every totally ordered set has a well-ordered cofinal subset
118595
Proving that a set is countable by finding a bijection
19924
Uncountable ordinals without power set axiom
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
102543
Real definition of "countable set"
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
139078
Infinite partition of $\mathbb N$ by infinite subsets
35692
The set of all finite subsets of the natural numbers is countable
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
144899
Do We Need the Axiom of Choice for Finite Sets?
66398
Union of a finite set and a countably infinite set is countably infinite
72190
Topological proof on discrete topology where $X$ is infinite