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1d
comment How to calculate $ \sum_{n=1}^{15}n(n!) = ? $
Uhm, sorry but this does not strike me as a good answer. It is a little involved, the first steps being completely useless: the point of the question is just the last step, which is not clearly motivated.
2d
comment To prove or refute: $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^{N} f\left( \frac{n}{N} \right) = 1$ then $f \in R\left( \left[ 0, 1 \right] \right)$
I meant the function that is equal to 1 on all rational numbers and 0 on all irrationals.
2d
comment To prove or refute: $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^{N} f\left( \frac{n}{N} \right) = 1$ then $f \in R\left( \left[ 0, 1 \right] \right)$
Also, I am not sure the result is true. Take $f(x)=\chi_\mathbb{Q\cap [0,1]}$. The limit is 1, but it is not Riemann integrable...
2d
comment To prove or refute: $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^{N} f\left( \frac{n}{N} \right) = 1$ then $f \in R\left( \left[ 0, 1 \right] \right)$
Well, to be rigorous, the limit is only one particular way to approximate the integral. One should work the details of showing that, independently of the partition of $[0,1]$ (assuming $h\to 0$ as $N\to\infty$), and independently on the choice of the point where you evaluate $f$ in each interval, the limit converges to the same number. So there is some detail to work out...
2d
comment To prove or refute: $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^{N} f\left( \frac{n}{N} \right) = 1$ then $f \in R\left( \left[ 0, 1 \right] \right)$
I'm not familiar with the notation $R([0,1])$. Is that Riemann integrable?
2d
comment Multiplying two Scalar dot products together
Are you asking how to write a dot product without writing a dot product? I'm confused...
2d
comment Gaussian Elimination vs matrix inversion
Ok, what do you mean by "matrix inversion"? Are you are talking about "inv(A)" in matlab?
Feb
9
comment Are there sets of zero measure and full Hausdorff dimension?
That's what I'm saying, you get a set of positive measure, which we are not interested in here. If the length removed is fixed and $\geq 1/3$, the measure of the Cantor set is 0. If is fixed and smaller than $1/3$, the measure of the cantor set is positive. Are you suggesting to build a Cantor set varying the length of the removed intervals? I am not sure how to do it in such a way that the measure is still 0 but the dimension is arbitrarily close to 1. Could you please write an example of one of the $C_n$?
Feb
9
comment Are there sets of zero measure and full Hausdorff dimension?
Uhm, varying the length of the intervals yields a "fat" Cantor set, with measure greater than zero. No?
Feb
8
reviewed Approve Quadratic Reciprocity - Legendre Symbols
Feb
2
comment Is my proof correct? Convex optimization
It works. As you said, all you need is the limit behavior of $\phi'(t)$ as $t$ approaches 0. You know $\phi'(t)\geq 0\forall t\in(0,1)$, hence the limit as $t\to 0$ of $\phi'(t)$ is nonnegative too.
Feb
2
reviewed Approve Simple Fraction needing explanation
Feb
2
comment Graph the function with an absolute minimum at (-2,-12), a local maximum at (0,3), a local minimum at (2,-1), and an absolute maximum at (4,9)?
I'd say 'graph' is pretty much a synonym of 'sketch', 'draw'. ;-)
Feb
2
answered Graph the function with an absolute minimum at (-2,-12), a local maximum at (0,3), a local minimum at (2,-1), and an absolute maximum at (4,9)?
Feb
1
answered How to solve this equation in spherical coordinates
Jan
26
reviewed Approve A kind of converse to the Jordan curve theorem
Jan
26
reviewed Edit How to calculate $\sum_{n \in P}\frac{1}{n^2}, P=\{n \in \mathbb{N}: \exists (a,b) \in\ \mathbb{N^+} \times \mathbb{N^+} \mbox{ with } a^2+b^2=n^2\}$
Jan
26
comment Why does an argument similiar to 0.999…=1 show 999…=-1?
I think this conversation had gone too far. Yes, there is a context where Geinmachi formula is correct, so we can't say that what he said "is false", per se. On the other hand, given the question, its tags, and the context, I doubt bringing up Ramanujan results can help the user who asked the question. To be more clear, a link right next to the formula would have explained the context. Or at least, I would have put a winky face, to give more of a "joke" connotation to the comment, which, as it was, I reckon could have been confusing for the person who asked the question.
Jan
26
reviewed Approve Set Closed or Open
Jan
23
revised Looking for “an easy to understand” proof for following Power series
added 5 characters in body