The difference between two rational numbers always is a rational number
87764
Prove that the difference between two rational numbers is rational
144244
Bound on difference between irrational square root and rational number
34710
Cardinality of Irrational Numbers
141273
When is $\sin(x)$ rational?
51649
prove there is no smallest positive rational number
117366
Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
138977
Infinitely many rational numbers between two different real numbers
44476
Can we ever get an irrational number by dividing two rational numbers?
107105
Is an irrational number odd or even?
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
150037
Finding the simplest rational in a closed interval
84558
Prove that the square root of a positive integer is either an integer or irrational
96647
Number theory: Problem involving rational numbers
154832
Show that there is always a proposition between two propositions logic
44250
rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
33998
Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$