Given that the rationals are countable and the denseness of $\mathbb{Q}$ in $\mathbb{R}$ how can $\mathbb{R}$ be uncountable?
34825
Intuitive explanation for how could there be "more" irrational numbers than rational?
19297
Is the cofinite topology on an uncountable set first countable?
153652
Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
135441
When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
83842
Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
43268
How to prove that the set of rational numbers are countable?
58471
Accumulation points of uncountable sets
146006
Uncountable $\sigma$-algebra
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
3645
Why Are the Reals Uncountable?
76240
How is $\epsilon_0$ countable?
127678
A partition of the unit interval into uncountably many dense uncountable subsets
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
121831
Proving that rational numbers are dense