Let $A$ be an infinite set and B a countable set, show that $\vert A \cup B \vert = \vert A \vert$
23442
Cardinality of the union of infinite and countable sets
103769
The Cartesian product of a finite number of countable sets is countable
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
81509
The cardinality of a countable union of countable sets, without the axiom of choice
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
102113
Proof that the number of proofs is countably infinite
9021
An infinite subset of a countable set is countable
48797
Proving Two Sets are Equal - Infinite Sets - Example
80096
Prove that the union of countably many countable sets is countable.
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
98151
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
138768
Showing that the family of Borel sets is countably generated
42794
Prove that functions map countable sets to countable sets
97697
Countable union of sets of cardinality $c$ has cardinality $c$
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?