Can we prove that the set of irrational numbers is uncountable without Cantor?
18360
Proof that the irrational numbers are uncountable
126199
Proof of $\pi$ not being a quadratic irrational number.
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
93389
Uncountable sets of Hausdorff dimension zero
154240
Inverse of Heine–Cantor theorem
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
4946
Non-existence of irrational numbers?
96204
Irrational number $\sqrt2$ proof
42066
Cantor - No set is equinumerous with its power set.
81509
The cardinality of a countable union of countable sets, without the axiom of choice
101028
Irrational numbers and Borel Sets
19297
Is the cofinite topology on an uncountable set first countable?
3636
Are any two uncountable sets similar to each other?
30796
Is the set of irrationals separable as a subspace of the real line?
124847
Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?
15110
About irrational logarithms
157513
How can I prove that these sets are countable infinite?