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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 Pringsheim’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))?
Sep
19
comment Limit of an integral containing a product
Are the integral limits 1 to infinity and do you mean N approaches infinity instead of of x?
Mar
30
comment If a rational number has a finite decimal representation, then it has a finite representation in base $b$ for any $b>1?$
Not true. 0.1 base 10 = 0.00011001100110011.... in base 2.