Prove that if $X$ is and infinite set and $Y$ is countable or finite, then $|X \cup Y| = |X|$
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
75019
Infinite Cartesian product of countable sets is uncountable
22240
Every infinite subset of a countable set is countable.
36281
A set is infinite iff it is equivalent to a proper subset of itself
24372
Infinite Set is Disjoint Union of Two Infinite Sets
157081
The cartesian product of a finite amount of countable sets is countable.
139247
Real Analysis - Prove a set is countable
151852
How to prove $A \subset B \iff A \cup B = B$
118595
Proving that a set is countable by finding a bijection
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
19297
Is the cofinite topology on an uncountable set first countable?
143735
Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
104550
Countable union of countable sets(ZF)
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.
125411
Infinite set always has a countably infinite subset