Rudy the Reindeer
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 Mar 17 comment If A is a subset of B, then the closure of A is contained in the closure of B. I thought so : ) Mar 17 answered The solution set of the equation $|2x - 3| = - (2x - 3)$ Mar 17 comment If A is a subset of B, then the closure of A is contained in the closure of B. It looks fine to me. Your proof is correct. : ) Mar 17 comment Computing a convolution using FFT I've not heard of approximating a function by its Fourier transform. You have $$(K \ast y) (x_m) = \sum_{j = 1}^N K(x_m - x_j) y_j$$ and $$\widehat{K \ast y} (x_m) = \hat{K}(x_m) \hat{y_m}$$ You can use FFT to compute these: do the multiplication and then do the inverse transform for each $m$. I don't understand how to use the Fourier transform to approximate a function. The other thing you could think about is to numerically approximate it: compute only a few of the function values and then use interpolation. Mar 16 comment Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. @tendua Here's a follow up question to BD's answer. Someone just pointed it out to me in chat. Mar 16 comment Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. @tendua No one got pinged by your "@All" ping, you need to ping using names. Sorry for the late reply. I voted to close your question because I thought the question I linked to answered your question. Now if you think your question is not answered and you'd like it to be reopened let us know. We can always vote to reopen it. Hope this helps. If you'd like to discuss any of the answers or anything else feel free to drop by the main chat room. Cheers Mar 15 comment Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. Sorry for being somewhat too quick on the trigger. Mar 12 revised Is $BC([0,1))$ ( space of bounded real valued continuous functions) separable? Is $BC([0,1))$ a subset of $BC([0,\infty))$? One "q" removed. Mar 11 revised What is the Discrete Time Fourier Transform of $x[n] = \frac{3\sin{(3\pi\frac{n}{4})}}{\pi n}$ deleted 1 characters in body Mar 10 comment Divergent sequence of derivatives @DidierPiau Yes. Thanks Didier. Mar 10 revised Divergent sequence of derivatives Mistake corrected. Mar 10 answered Divergent sequence of derivatives Mar 8 awarded Revival Mar 8 answered Determine the closure of the set $K=\{\frac{1}{n}\mid n\in\mathbb N\}$ under each of topologies Mar 8 revised Is there something like Cardano's method for a SOLVABLE quintic. Typo corrected. Mar 5 revised Construction of “pathological” measures Minor English mistakes corrected. Mar 5 comment About product measure and Tonelli-Fubini Theorem: Show that H is closed under increasing limit and differences. Thank you. But I still don't fully understand: We defined $\mathcal{H}$ in terms of the functions $f_C : x \mapsto Q[{C(x)}]$, namely we take it to be all the sets $C$ that make $f_C$ measurable. Since $Q$ is a probability measure, $f_C$ is a function into $[0,1]$. Now for some reason that I don't yet see, $f_C^{-1}$ maps (Lebesgue?) measurable sets in $[0,1]$ to sets in $\mathcal{E}$. Is $\mathcal{A} = \mathcal{H}$? Mar 5 revised Decreasing sequence of sets Typos corrected. Mar 4 comment About product measure and Tonelli-Fubini Theorem: Show that H is closed under increasing limit and differences. So if $C$ is measurable, the slice $C(x)$ is measurable? Mar 4 comment Advice for writing good mathematics? I'll recommend what someone of the community recommended to me: J. Milne's page: Tips for authors. and D. Goss: Some Hints on Mathematical Style based on tips by Serre.