On the size of rational numbers and Irrational numbers.
18360
Proof that the irrational numbers are uncountable
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
147363
Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?
30411
The closure of the irrational numbers on $\mathbb{R}$
111898
Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?
13550
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
95702
Remarkable/unexpected rational numbers
15110
About irrational logarithms
96204
Irrational number $\sqrt2$ proof
30105
Multiples of an irrational number forming a dense subset
24706
Is there a rational number between any two irrationals?
125267
Prove that $2^{1/2}$ is irrational
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
87410
Are there real numbers that are neither rational nor irrational?
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?