query: The intuition behind choosing the number $e = \exp(1)$
positive_passages.docid: 40286
positive_passages.text: What's so "natural" about the base of natural logarithms?
negative_passages.docid: 67410
negative_passages.text: Why does this expected value simplify as shown?
negative_passages.docid: 51869
negative_passages.text: Why does $\;\lim_{n\to \infty }\frac{n}{n!^{1/n}}=e$?
negative_passages.docid: 146033
negative_passages.text: Intuitive Proof of the Chain Rule in 1 Variable
negative_passages.docid: 35277
negative_passages.text: Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
negative_passages.docid: 147159
negative_passages.text: Determine the set of values of $\exp(1/z)$ for $0<|z|<r$
negative_passages.docid: 72735
negative_passages.text: Understanding the proof of a formula for $p^e\Vert n!$
negative_passages.docid: 118195
negative_passages.text: How does one prove that $e$ exists?
negative_passages.docid: 113526
negative_passages.text: Why intuitively does $\mathbb E(\frac d {d\theta}\log p_\theta(x))=0$?
negative_passages.docid: 41648
negative_passages.text: The Intuition behind l'Hopitals Rule
negative_passages.docid: 69943
negative_passages.text: why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
negative_passages.docid: 78869
negative_passages.text: On the justification of the result of a limit utilizing little-o. (quick question)
negative_passages.docid: 109839
negative_passages.text: What is the Necessity of $...$ Around Numbers?
negative_passages.docid: 92912
negative_passages.text: Why is the number $e$ so important in mathematics?
negative_passages.docid: 21923
negative_passages.text: Prove that $\exp(x)>0$ using only formal definition of exp
negative_passages.docid: 48332
negative_passages.text: Why does the minimum value of $x^x$ equal $1/e$?
negative_passages.docid: 46144
negative_passages.text: Understanding imaginary exponents