query: How to explain irrational numbers to laymen?
positive_passages.docid: 22762
positive_passages.text: How can adding an infinite number of rationals yield an irrational number?
negative_passages.docid: 58284
negative_passages.text: How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
negative_passages.docid: 134264
negative_passages.text: How to get exact Rationalize of a decimal number?
negative_passages.docid: 6275
negative_passages.text: How can you prove that the square root of two is irrational?
negative_passages.docid: 153976
negative_passages.text: Do complex quantities and irrational numbers exist in nature?
negative_passages.docid: 23164
negative_passages.text: Why are irrational numbers uncountable and rationals countable?
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: 141424
negative_passages.text: $\log_7 n$ is either an integer or an irrational number
negative_passages.docid: 118374
negative_passages.text: Is there a proof that $\pi$ is an irrational number?
negative_passages.docid: 120906
negative_passages.text: Is there a proof that $\pi \times e$ is irrational?
negative_passages.docid: 28230
negative_passages.text: What bizarrities lurk within the decimal expansion of an irrational number?
negative_passages.docid: 41767
negative_passages.text: Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
negative_passages.docid: 138446
negative_passages.text: Proving that there exists an irrational number in between any given real numbers
negative_passages.docid: 125267
negative_passages.text: Prove that $2^{1/2}$ is irrational
negative_passages.docid: 30523
negative_passages.text: A binary irrational with bits defined by primes
negative_passages.docid: 87410
negative_passages.text: Are there real numbers that are neither rational nor irrational?
negative_passages.docid: 122226
negative_passages.text: Incorrect logic in popular proof of the irrationality of $\sqrt2$?