Any infinite set contains a countable subset. Why is my proof wrong? (Axiom of Choice)
134319
When induction proofs need a choice function
14972
Cardinality of Vitali sets: countably or uncountably infinite?
136755
Direct proof of empty set being subset of every set
42794
Prove that functions map countable sets to countable sets
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
762
Proving every infinite set $S$ contains a denumerable subset
84936
The set of all finite sequences of members of a countable set is also countable
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
78290
Countable axiom of choice: why you can't prove it from just ZF
70940
Homework - set theory infinite union
74860
Why is the empty set a subset of every set?
41192
Neatest proof that set of finite subsets is countable?
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
118595
Proving that a set is countable by finding a bijection
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
103769
The Cartesian product of a finite number of countable sets is countable