query: In real numbers, the number of rational numbers is more or the number of irrational numbers is more?
positive_passages.docid: 23164
positive_passages.text: Why are irrational numbers uncountable and rationals countable?
negative_passages.docid: 158730
negative_passages.text: Is $\ln(\ln(n))$ irrational for any integer $n>1$?
negative_passages.docid: 124448
negative_passages.text: For every real number $a$ there exists a sequence $r_n$ of rational numbers such that $r_n$ approaches $a$.
negative_passages.docid: 152172
negative_passages.text: Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
negative_passages.docid: 87764
negative_passages.text: Prove that the difference between two rational numbers is rational
negative_passages.docid: 96647
negative_passages.text: Number theory: Problem involving rational numbers
negative_passages.docid: 102583
negative_passages.text: Infinite number of rationals between any two reals.
negative_passages.docid: 29780
negative_passages.text: If $x$ is a positive rational but not an integer, is $x^x$ irrational?
negative_passages.docid: 53945
negative_passages.text: The square root of a prime number is irrational
negative_passages.docid: 24706
negative_passages.text: Is there a rational number between any two irrationals?
negative_passages.docid: 30105
negative_passages.text: Multiples of an irrational number forming a dense subset
negative_passages.docid: 156946
negative_passages.text: The set of real numbers is a subset of the set of complex numbers?
negative_passages.docid: 43283
negative_passages.text: More numbers between $[0,1]$ or $[1,\infty)$?
negative_passages.docid: 1877
negative_passages.text: Can an irrational number raised to an irrational power be rational?
negative_passages.docid: 41767
negative_passages.text: Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
negative_passages.docid: 78287
negative_passages.text: Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
negative_passages.docid: 98666
negative_passages.text: Continuity defined for rational and irrational numbers