query: Example 7.4 from Rudin
positive_passages.docid: 15330
positive_passages.text: Double limit of $\cos^{2n}(m! \pi x)$ at rationals and irrationals
negative_passages.docid: 49505
negative_passages.text: Problem 1.1.5 from Hatcher's
negative_passages.docid: 87467
negative_passages.text: Finding some missing subfields of a splitting field of $x^4-7$
negative_passages.docid: 29218
negative_passages.text: I totally don't get the result from the R 'order' example
negative_passages.docid: 58673
negative_passages.text: Elements of order 5 in $S_7$, odd permutations of order 4 in $S_4$, and find a specific permutation in $S_7$
negative_passages.docid: 30311
negative_passages.text: Base change and irreducibility/reducedness/connectedness in Qing Liu's book (3.2.7 and 3.2.11 using 3.2.6)
negative_passages.docid: 91222
negative_passages.text: Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
negative_passages.docid: 139371
negative_passages.text: Sums of complex numbers - proof in Rudin's book
negative_passages.docid: 82443
negative_passages.text: Question about series rearrangement in Baby Rudin (theorem 3.54).
negative_passages.docid: 55259
negative_passages.text: ArcTan[z] and ArcTan[x,y], Restriction and Conversion
negative_passages.docid: 120213
negative_passages.text: Example $x$, $y$ and $z$ values for $x\uparrow^\alpha y=z$ where $\alpha\in \Bbb R-\Bbb N$
negative_passages.docid: 20377
negative_passages.text: Example 4.21 in Baby Rudin: Why is the inverse of this function not continuous at this point?
negative_passages.docid: 133775
negative_passages.text: Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
negative_passages.docid: 42539
negative_passages.text: Theorem 3.37 in Baby Rudin: $\lim\inf\frac{c_{n+1}}{c_n}\leq\lim\inf\sqrt[n]{c_n}\leq\lim\sup\sqrt[n]{c_n}\leq \lim\sup\frac{c_{n+1}}{c_n}$
negative_passages.docid: 41244
negative_passages.text: $\zeta_5$ has degree $4$ over $\mathbb{Q}$ and $\zeta_7$ has degree $6$ over $\mathbb{Q}$
negative_passages.docid: 94397
negative_passages.text: Example of a non-splitting exact sequence $0 → M → M\oplus N → N → 0$
negative_passages.docid: 138331
negative_passages.text: questions about Rudin's summation by parts