Let $S$ be an infinite set. Then there is a set $A\subset S$ such that $A\sim \mathbb{N}$.
762
Proving every infinite set $S$ contains a denumerable subset
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
132537
Class of sets of a given infinite cardinality
24266
Accumulation points of the set $S=\{(\frac {1} {n}, \frac {1} {m}) \space m, n \in \mathbb N\}$
81843
Sequences of sets property
92571
Sets with no asymptotical density over $\mathbb N$
20085
What's the cardinality of all sequences with coefficients in an infinite set?
9651
Cardinality of cartesian product of an infinite set with N
59535
Prove that there exists such a set of $n$ positive integers
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
66334
How is every subset of the set of reals with the finite complement topology compact?
62208
If $A$ is a non-empty set, then $A \notin A$
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
44974
Infinite set and countable subsets
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?