Let M be an infinite set and A be countable prove that there is a 1-1 correspondence between $A\cup M$ and M
132868
Bijection between an infinite set and its union of a countably infinite set
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
119624
A Dedekind infinite set has a countably infinite proper subset
12436
The cardinality of the set of all finite subsets of an infinite set
41192
Neatest proof that set of finite subsets is countable?
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
125962
The set $A'$ is closed in a $T_1$ space
128118
Is the cofinite topology on a countable set first countable?
88904
Help with a proof. Countable sets.
157513
How can I prove that these sets are countable infinite?
99478
countably infinite union of countably infinite sets is countable
149673
Cardinality of an infinite union of finite sets
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality