Formal proof that $N$ is the smallest infinite set
94413
Proving Dedekind finite implies finite assuming countable choice
117658
A set with n elements has 2^n subsets
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
132868
Bijection between an infinite set and its union of a countably infinite set
107614
Partitioning an infinite set
23608
Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem.
120712
Is there a way to define the "size" of an infinite set that takes into account "intuitive" differences between sets?
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
44974
Infinite set and countable subsets
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
16826
prove that every infinite subset of compact set H has a limit point (Explanation)
78117
Closed property of nonempty finite set
28391
Prove the compactness of a set B
60004
Why is $\omega$ the smallest $\infty$?
136755
Direct proof of empty set being subset of every set
24050
Characterization of the Closure of a Set