By using a diagonal argument, show that the powerset $P(N) = (S|S ⊆ N)$ is uncountable.
6681
How does Cantor's diagonal argument work?
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
88079
R has an uncountable number of distinct dense subsets.
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
60359
Proving that these two sets are denumerable.
44497
Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?
129205
A question about uncountable, dense sets in R
71133
prove inequlity about cardinality power sets
67064
Uncountable minus countable set is uncountable
117658
A set with n elements has 2^n subsets
87830
Relating the union of the power set of a set to the set itself
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
76635
Proof through combinatorial argument
118595
Proving that a set is countable by finding a bijection
116501
How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic?