Prove or disprove irrational numbers
112539
Can I disprove a claim using the contrapositive?
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
64885
Irrational and rational sequence proof
1877
Can an irrational number raised to an irrational power be rational?
77129
Density of irrationals
40009
Show that $e^{\sqrt 2}$ is irrational
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
65300
Why is $\pi$ irrational?
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
31744
Proving that there is an irrational number between any two unequal rational numbers.
63960
proving "e" irrational using convergent series
138446
Proving that there exists an irrational number in between any given real numbers
151325
(How to/Can I) show irrational numbers?
44476
Can we ever get an irrational number by dividing two rational numbers?
100319
Functional equation with strange property about irrational numbers
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?