query: One rational between two reals
positive_passages.docid: 24706
positive_passages.text: Is there a rational number between any two irrationals?
negative_passages.docid: 100862
negative_passages.text: Polynomials with rational zeros
negative_passages.docid: 139614
negative_passages.text: Polynomial bounded real part of an entire function
negative_passages.docid: 158066
negative_passages.text: Prove $2^{1/3}$ is irrational.
negative_passages.docid: 87764
negative_passages.text: Prove that the difference between two rational numbers is rational
negative_passages.docid: 84374
negative_passages.text: Rational function with absolute value $1$ on unit circle
negative_passages.docid: 98666
negative_passages.text: Continuity defined for rational and irrational numbers
negative_passages.docid: 8255
negative_passages.text: Real polynomials from repunits to repunits ( Putnam 2007 A4)
negative_passages.docid: 55509
negative_passages.text: Factor a polynomial over the reals
negative_passages.docid: 22408
negative_passages.text: Jutifying: irrational + rational = irrational
negative_passages.docid: 15104
negative_passages.text: Show that $\big|\frac{a-b}{1-\overline{a}b}\big|=1$, when either $|a|=1$ or $|b|=1$.
negative_passages.docid: 39156
negative_passages.text: Concerning what is between two consecutive squares.
negative_passages.docid: 105445
negative_passages.text: Are the rationals a closed or open set in $\mathbb{R}$?
negative_passages.docid: 117366
negative_passages.text: Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
negative_passages.docid: 68456
negative_passages.text: Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
negative_passages.docid: 64885
negative_passages.text: Irrational and rational sequence proof
negative_passages.docid: 144244
negative_passages.text: Bound on difference between irrational square root and rational number