for any infinite set A, |A| >= |N|
91237
Every infinite set contains a countable subset
102113
Proof that the number of proofs is countably infinite
82009
Prove that every totally ordered set has a well-ordered cofinal subset
42095
Existence in ZF of a set with countable power set
81682
Proving the algebraic set corresponding to a polynomial is infinite.
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
41192
Neatest proof that set of finite subsets is countable?
53593
Limits of sequences of sets
151928
How to prove that $N\setminus A$ is finite?
92249
Every finite set contains its supremum: proof improvement.
70940
Homework - set theory infinite union
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
119624
A Dedekind infinite set has a countably infinite proper subset
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
12404
Union of definable sets
146560
Is there any uncountably infinite set that does not generate the reals?
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists