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 Nov 7 comment What is the output of an indicator function $\mathbb{1}_{A_i}(w)$ over some set $X=\{w_1,…,w_n\}$? 1 if $w \in A_i$, 0 otherwise. Nov 9 comment Suffix string starting at $i$ That's what it sounds like. Feb 19 comment If the cost per minute is $\$0.032$, is the cost per hour$\$1.92$ or $1.92$¢? Since you started with dollars, it won't magically change to cents. If garlic is $0.50 each, buying 10 of them will be$0.50*10 = $5.00 not 5.00¢. If you want to convert dollar to cents you have to multiply by 100¢/$1. See khanacademy.org/math/cc-sixth-grade-math/… Jan 25 comment Is computer science a branch of mathematics? I did not criticize computer science, the internet, or masturbation. I criticize your philosophic post which conveys nothing to the reader despite the use of a thousand words. It was written for your pleasure only. Jan 24 comment Is computer science a branch of mathematics? @SpYk3HH I agree. There is a point where reductionism becomes fruitless. Jan 10 comment Why are mathematical proofs that rely on computers controversial? "Also computers give connected people advantage, while without computers math is very open." I don't think this is a good reason at all. It is like saying math is more "open" if nobody referred to books, journals, or colleagues because books, journals, and colleagues are accessible only to "connected people". Jan 8 comment Quadratic formula - math error For classifying the point, it might be more useful to complete the square: x^2-2x+2 = (x +/- something)^2 +/- a constant. Then the nature of x=1 will be revealed. Jan 4 comment Prove that $4$ is the only solution to $2+2$. "Mom, if you don't believe me, don't use my result!" Dec 17 comment Best way to generalize a distribution of data into smaller subsets? You might want to search for "clustering" algorithms. Nov 20 comment Factors of a number. A number is called "even" if 2 is a factor. A number is called "odd" if 2 is not a factor. 70 is even because 2 is a factor but the other factors are 5 and 7. And you can't get 5 or 7 from 70/2, 70/4, 70/8, etc. Knowing a number is even gives you no other information other than 2 is a factor. Nov 20 comment Showing that a functor is Exact What did you use to generate that beautiful diagram? Asymptote? Nov 14 comment Continued fraction with alternative signs Not a complete answer but Pringsheimâ€™s Theorem says that $|a_i| \ge 2$ is sufficient for convergence. See DLFM 1.12. Jul 7 comment Computing the value of logarithmic series: $Q(s,n) = \ln(1)^s + \ln(2)^s + \ln(3)^s + \cdots+ \ln(n)^s$ yes it does approach zero because if you calculate the error term or Euler-Maclaurin, you will see it is bounded by the first derivative (ie $s(\log(n))^{s-1}/n$). Jul 7 comment Computing the value of logarithmic series: $Q(s,n) = \ln(1)^s + \ln(2)^s + \ln(3)^s + \cdots+ \ln(n)^s$ You should expand your answer. Using just the first 3 terms of the Euler-Macclaurin formula, you can show that the error is less than $\frac{s}{12n}(\log(n))^{s-1}$ for $s\gt 1$. Unfortunately the error bound doesn't start going down until $n \gt e^{s-1}$. May 21 comment How to calculate this multi-integral? The sign is wrong. The last integral should be +1/2 sin(z). May 4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ @math110, it is the same. You only need to show $n! > 2e^{-\lambda n} \int^{\lambda n}_0 (\lambda n -t)^n e^t dt$ which follows basically what you have already. May 4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ @math110, I meant replace your argument of $x=n$ with $x=\lambda n$ and you will arrive at the same conclusion you have for $x=n$. May 4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ I think you can do this by letting $x := \lambda n$ where $0 \lt \lambda \le 1$. All your inequalities will remain true. Jan 16 comment Lost on algebra notation @Clayton, I think that's an exaggeration. Most undergrad number theory books don't require much algebra prerequisites if any (eg, old books like Landau and Hardy/Wright). Dec 24 comment Proving that $\left(1+\frac{z_{1}}{z_{2}}\right)\left(1+\frac{z_{2}}{z_{3}}\right)…\left(1+\frac{z_{n}}{z_{1}}\right)\in\mathbb R$ should be 2\cos(t_i-t_j)e^(i(t_i-t_j))?