If $a$ is an infinite cardinal number, prove that $\aleph_0 + a = a$
23442
Cardinality of the union of infinite and countable sets
109968
Let $X= \{ A \subset \mathbb{N} : \mathbb{N} \backslash A \text{ is finite}\}$. What is the cardinality of $X$? Prove it.
102113
Proof that the number of proofs is countably infinite
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
3111
How to prove that if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+...+a_n}{n}=A$
145397
How to prove that for every $i$, $a_i = i$
156006
Cardinality of set containing all infinite subsets of $\mathbb{Q}$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
30519
"Real" cardinality, say, $\aleph_\pi$?
41783
Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
12436
The cardinality of the set of all finite subsets of an infinite set
86421
Proof of the definition of cardinal exponentiation
45218
Comparing the two cardinals $\aleph_0^{\aleph_0}$ and $2^{\aleph_0}$
4782
Can we distinguish $\aleph_0$ from $\aleph_1$ in Nature?
104744
Can sets of cardinality $\aleph_1$ have nonzero measure?
149673
Cardinality of an infinite union of finite sets
48278
Inequality about infinite cardinals