query: Algebraic numbers in the interval $[0,1]$
positive_passages.docid: 25509
positive_passages.text: evaluation of an integral involving algebraic numbers
negative_passages.docid: 34710
negative_passages.text: Cardinality of Irrational Numbers
negative_passages.docid: 134896
negative_passages.text: Enlightening proof that the algebraic numbers form a field
negative_passages.docid: 1117
negative_passages.text: Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
negative_passages.docid: 45216
negative_passages.text: Cardinality of $[0,1]$
negative_passages.docid: 153107
negative_passages.text: Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
negative_passages.docid: 33792
negative_passages.text: Numbers to the Power of Zero
negative_passages.docid: 30411
negative_passages.text: The closure of the irrational numbers on $\mathbb{R}$
negative_passages.docid: 82628
negative_passages.text: Cardinality of a set of closed intervals
negative_passages.docid: 81264
negative_passages.text: Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
negative_passages.docid: 81150
negative_passages.text: Positive integer multiples of an irrational mod 1 are dense
negative_passages.docid: 2396
negative_passages.text: Order-preserving injections of ordinals into $[0,1]$
negative_passages.docid: 124511
negative_passages.text: The set of algebraic numbers is a field.
negative_passages.docid: 151225
negative_passages.text: Solved Problems in Algebraic Number Theory
negative_passages.docid: 33705
negative_passages.text: Is $0$ a natural number?
negative_passages.docid: 30192
negative_passages.text: How far are the $p$-adic numbers from being algebraically closed?
negative_passages.docid: 39692
negative_passages.text: The length of an interval covered by an infinite family of open intervals