query: Is $\arctan2$ irrational?
positive_passages.docid: 26109
positive_passages.text: Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
negative_passages.docid: 44600
negative_passages.text: How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
negative_passages.docid: 30411
negative_passages.text: The closure of the irrational numbers on $\mathbb{R}$
negative_passages.docid: 106242
negative_passages.text: Why no common factors in proving root 2 is irrational?
negative_passages.docid: 101028
negative_passages.text: Irrational numbers and Borel Sets
negative_passages.docid: 37642
negative_passages.text: Why is $\pi$ irrational if it is represented as $C/D$?
negative_passages.docid: 34710
negative_passages.text: Cardinality of Irrational Numbers
negative_passages.docid: 4573
negative_passages.text: Explicitly finding the sum of $\arctan(1/(n^2+n+1))$
negative_passages.docid: 15330
negative_passages.text: Double limit of $\cos^{2n}(m! \pi x)$ at rationals and irrationals
negative_passages.docid: 30523
negative_passages.text: A binary irrational with bits defined by primes
negative_passages.docid: 19216
negative_passages.text: Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?
negative_passages.docid: 150576
negative_passages.text: When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?
negative_passages.docid: 40009
negative_passages.text: Show that $e^{\sqrt 2}$ is irrational
negative_passages.docid: 11069
negative_passages.text: Deciding whether $2^{\sqrt2}$ is irrational/transcendental
negative_passages.docid: 7801
negative_passages.text: Can you raise a number to an irrational exponent?
negative_passages.docid: 1877
negative_passages.text: Can an irrational number raised to an irrational power be rational?
negative_passages.docid: 5747
negative_passages.text: $\cos(\arcsin(x)) = \sqrt{1 - x^2}$. How?