If $B$ is an uncountable set and $A$ is a countable set, then prove that $B$ is similar to $B-A$.
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
110635
Proving $\mathbb{N}^k$ is countable
23907
$Seq (\mathbb{N})$ of all finite sequences of elements of $\mathbb{N}$ is countable.
63678
Let $A$ and $B$ be countable sets. Is there any function $f$ such that a certain condition holds for an uncountable number of functions $g$?
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
43268
How to prove that the set of rational numbers are countable?
66301
The cardinality of the set of countably infinite subsets of an infinite set
44974
Infinite set and countable subsets
99599
Uncountable and countable
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
75019
Infinite Cartesian product of countable sets is uncountable
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
28391
Prove the compactness of a set B
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
67064
Uncountable minus countable set is uncountable
84936
The set of all finite sequences of members of a countable set is also countable