Proving that an irrational number exists near every rational number
138446
Proving that there exists an irrational number in between any given real numbers
86988
Cardinality of the Irrationals
67031
use contradiction to prove that the square root of $p$ is irrational
158368
Irrationals: A Group?
98666
Continuity defined for rational and irrational numbers
101028
Irrational numbers and Borel Sets
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
65895
Irrationality proofs not by contradiction
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
132478
Prove that continuous functions mapping irrationals to rationals must be constant
109175
Why is it hard to prove whether $\pi+e$ is an irrational number?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
30478
How to prove that a number is irrational
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
139979
Proof there is a rational between any two reals
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational