Improve and complete the proof of : If $X$ is infinite and $I \subseteq N$, then $ X\cup I \approx X$
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
92249
Every finite set contains its supremum: proof improvement.
91523
Prove this limit as $x\to\infty$
12436
The cardinality of the set of all finite subsets of an infinite set
28391
Prove the compactness of a set B
762
Proving every infinite set $S$ contains a denumerable subset
47434
Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
102048
Closure of a compact set in Regular space $ X $
156006
Cardinality of set containing all infinite subsets of $\mathbb{Q}$
102478
$X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
4467
Proving Cantor's theorem
33310
Proving that the set of limit points of a set is closed
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
18907
Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
52614
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X