How to prove that $x=0.1234567891011\dots $ is irrational?
30478
How to prove that a number is irrational
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
77129
Density of irrationals
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
134264
How to get exact Rationalize of a decimal number?
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
138446
Proving that there exists an irrational number in between any given real numbers
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
19076
If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
21237
$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational
31744
Proving that there is an irrational number between any two unequal rational numbers.
4946
Non-existence of irrational numbers?
67605
Different proof that $\sqrt{2}$ is irrational
114793
Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
86988
Cardinality of the Irrationals