Why does this proof that the set of all finite subsets of N is a countable set not work for the set of all subsets of N?
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
151928
How to prove that $N\setminus A$ is finite?
88904
Help with a proof. Countable sets.
75019
Infinite Cartesian product of countable sets is uncountable
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
132778
All distances are rational prove the set is countable
19297
Is the cofinite topology on an uncountable set first countable?
136306
Let $A$ be a finite set and let $B$ be a subset of $A$ with $|A|=n$,$|B|=m$ and $0<m<n$. Count the subsets of $A$ containing $ B.$
66398
Union of a finite set and a countably infinite set is countably infinite
128437
How to prove that a finite set is countable
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
118595
Proving that a set is countable by finding a bijection
63276
Is an arbitrary union of a chain of countable sets countable?
51617
What is the proof that the total number of subsets of a set is $2^n$?
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
102543
Real definition of "countable set"
3072
If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?