query: Why is $\ln 20$ so close to $3$?
positive_passages.docid: 148094
positive_passages.text: Show that $e^3 > 20$
negative_passages.docid: 57647
negative_passages.text: Prove that s is finite and find an n so large that $S_n$ approximate s to three decimal places.
negative_passages.docid: 58570
negative_passages.text: Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?
negative_passages.docid: 30172
negative_passages.text: Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10?
negative_passages.docid: 66364
negative_passages.text: Why is $(\sqrt{2}+\sqrt{3})^{2008}$ so close to an integer?
negative_passages.docid: 125506
negative_passages.text: Why can I get two different results when calculating $\int \ln(z) \,dz$?
negative_passages.docid: 108588
negative_passages.text: Improving bound on $\sqrt{2 \sqrt{3 \sqrt{4 \ldots}}}$
negative_passages.docid: 98380
negative_passages.text: $x^{20}=1$ for all $x\in U(100)$
negative_passages.docid: 1148
negative_passages.text: Curious limit of a sequence used to prove Etemadi's SLLN
negative_passages.docid: 36757
negative_passages.text: I can't determine the maximum natural number which is unable to be represented as $17\times x+23\times y$
negative_passages.docid: 32984
negative_passages.text: why 64 is equal to 65 here?
negative_passages.docid: 129824
negative_passages.text: For what $a \in \Bbb R$ does $\neg(3a>21\implies a \leq 5)$ hold?
negative_passages.docid: 140990
negative_passages.text: Could anyone explain to me how did we get this result? This is simple example but I'm struggling with little o notation in general.
negative_passages.docid: 140409
negative_passages.text: Prove that $\sqrt{n} > \ln n$
negative_passages.docid: 49368
negative_passages.text: Why does factoring eliminate a hole in the limit?
negative_passages.docid: 103988
negative_passages.text: Prove that $\tan20^°\tan40^°\tan60^°\tan80^°=3$
negative_passages.docid: 15821
negative_passages.text: $\ln(x^2)$ vs $2\ln x$