Show that the set of all irrationals is not countable
18360
Proof that the irrational numbers are uncountable
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
128437
How to prove that a finite set is countable
136321
Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
154474
Image of countable and uncountable sets
65895
Irrationality proofs not by contradiction
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
71922
Prove Uncountable set minus a countable set is uncountable
155777
Show that infinite Cartesian product is uncountable
132778
All distances are rational prove the set is countable
91237
Every infinite set contains a countable subset
130981
Co-countable measure on uncountable set
68139
Show that the set of polynomials with rational coefficients is countable.
127362
How do I prove that there doesn't exist a set whose power set is countable?
23164
Why are irrational numbers uncountable and rationals countable?
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?