query: Compare between $\ln(2)$, $\ln(-2)$
positive_passages.docid: 146248
positive_passages.text: What did Johann Bernoulli wrong in his proof of $\ln z=\ln (-z)$?
negative_passages.docid: 14487
negative_passages.text: Does $\sum_{n=2}^\infty (n\ln n)^{-1}$ diverge?
negative_passages.docid: 53830
negative_passages.text: Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x)\,dx $
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 7041
negative_passages.text: Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$
negative_passages.docid: 46825
negative_passages.text: The identity det(A) = exp(Tr(ln(A)) for A general
negative_passages.docid: 155884
negative_passages.text: What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
negative_passages.docid: 40534
negative_passages.text: What is $(-1)^{\frac{2}{3}}$?
negative_passages.docid: 70415
negative_passages.text: Comparison between the $\ell_1$ and $\ell_2$ norms
negative_passages.docid: 5650
negative_passages.text: Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$
negative_passages.docid: 55494
negative_passages.text: Proving Asymptotic Barrier - O notation for $\ln(n!)$
negative_passages.docid: 145719
negative_passages.text: Similarity between $A$ and $B (2\times 2)$.
negative_passages.docid: 108528
negative_passages.text: How to compare functions?
negative_passages.docid: 46310
negative_passages.text: Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
negative_passages.docid: 6304
negative_passages.text: Evaluate $\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $
negative_passages.docid: 44059
negative_passages.text: Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
negative_passages.docid: 113411
negative_passages.text: If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?