query: Ramanujan's radical and how we define an infinite nested radical
positive_passages.docid: 19174
positive_passages.text: Definition of convergence of a nested radical $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$?
negative_passages.docid: 35855
negative_passages.text: Closed form for an infinite product
negative_passages.docid: 47596
negative_passages.text: An infinite series plus a continued fraction by Ramanujan
negative_passages.docid: 157771
negative_passages.text: Nested exponent modulus, $2^{2^{517}} \pmod {23}$
negative_passages.docid: 127727
negative_passages.text: De Moivre Complex Roots: Definition of $i$ or $\sqrt {-1}$
negative_passages.docid: 12949
negative_passages.text: Inductive Proof of Euler's Formula $v-e+r=2$
negative_passages.docid: 41312
negative_passages.text: Question on primitive roots of unity
negative_passages.docid: 18003
negative_passages.text: Standard example where Jacobson radical not equal nilradical
negative_passages.docid: 24008
negative_passages.text: Infinitely many primes of the form $\lfloor \sqrt {3} \cdot n \rfloor $?
negative_passages.docid: 129430
negative_passages.text: Hardy-Ramanujan theorem's "purely elementary reasoning"
negative_passages.docid: 125876
negative_passages.text: Sum and Product of Infinite Radicals
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 115270
negative_passages.text: What are the generators of $(\mathbb{R},+)$?
negative_passages.docid: 133286
negative_passages.text: Conjugates of radicals
negative_passages.docid: 75625
negative_passages.text: Complete residue system proof