query: Is it possible to represent every irrational number as a (limit of) an infinite sum of rational numbers?
positive_passages.docid: 21606
positive_passages.text: Can all real numbers be represented by the sum of a convergent series?
negative_passages.docid: 102583
negative_passages.text: Infinite number of rationals between any two reals.
negative_passages.docid: 109175
negative_passages.text: Why is it hard to prove whether $\pi+e$ is an irrational number?
negative_passages.docid: 8626
negative_passages.text: The limit of a sum (a Riemann sum?)
negative_passages.docid: 15110
negative_passages.text: About irrational logarithms
negative_passages.docid: 4946
negative_passages.text: Non-existence of irrational numbers?
negative_passages.docid: 151308
negative_passages.text: Is it possible to turn infinite sums into infinite products?
negative_passages.docid: 52486
negative_passages.text: Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
negative_passages.docid: 1098
negative_passages.text: Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge?
negative_passages.docid: 3790
negative_passages.text: Rational + irrational = always irrational?
negative_passages.docid: 62792
negative_passages.text: Can sum of a rational number and its reciprocal be an integer?
negative_passages.docid: 83145
negative_passages.text: Sum of rational numbers
negative_passages.docid: 12547
negative_passages.text: Is it okay to "ignore" small numbers in limits where $x$ approaches infinity?
negative_passages.docid: 125860
negative_passages.text: Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
negative_passages.docid: 152512
negative_passages.text: What is the ratio of rational to irrational real numbers?
negative_passages.docid: 89814
negative_passages.text: Limit of a Piecewise Function defined on Rationals and Irrationals
negative_passages.docid: 69439
negative_passages.text: Infinite Sum of algebraic expression