Activity for The Amplitwistâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #291159 |
The [Wikipedia](https://en.wikipedia.org/wiki/Separation_of_variables) article on "separation of variables" might be a good starting point to figure out an answer. (more) |
— | 5 days ago |
| Comment | Post #291317 |
Thank you for the answer! I'm still digesting the arguments, it's all a bit too quick for me. I may ping you for clarification in a few days, once I get some time. (more) |
— | 14 days ago |
| Comment | Post #291301 |
@#36356 Yes, the $0$-simplex has nonempty interior. Here is a more precise definition of $\overset{\circ}{\Delta}{}^n$ from Hatcher (page 103).
> If we delete one of the $n+1$ vertices of an $n$-simplex $[v_0,\dotsm,v_n]$, then the remaining $n$ vertices span an $(n-1)$-simplex, called a **face** of... (more) |
— | 20 days ago |
| Comment | Post #291056 |
Perhaps the "pathological imbeddings" can only be obtained by imbedding into two-dimensional locally Euclidean spaces that are not Hausdorff, or paracompact, or second-countable (or any similar nice properties). Cf. [Topological manifold - Wikipedia](https://en.wikipedia.org/wiki/Topological_manifold... (more) |
— | about 2 months ago |
| Comment | Post #290771 |
This post seems to have been deleted by the moderators of r/math. (more) |
— | 3 months ago |
| Comment | Post #280864 |
@Technologicallyilliterate Added a few words to my answer. (more) |
— | about 3 years ago |
| Comment | Post #280866 |
This is some meaty stuff, and I love it. Thank you for writing it up! (more) |
— | about 3 years ago |
| Comment | Post #280864 |
@Technologicallyilliterate Sure, I'll try to add something tomorrow. (more) |
— | about 3 years ago |
| Comment | Post #280851 |
Just transcribe the content of the image in addition to posting the image. It's good that you want to ensure that you're not mistyping the solution manual, but presenting text as images makes it difficult or impossible for people with accessibility issues to know what you're referring to. (more) |
— | about 3 years ago |
| Comment | Post #280842 |
Taking another look at the displayed equation in my post, I think I can take $G_1 = 0$ and $G_2 = \int F_3(x, y)\\, dx$ (or the other way around) provided the integral exists. This seems to provide some criterion at least in the $\mathbb{R}^2$ case. (more) |
— | about 3 years ago |
| Comment | Post #280630 |
One has to escape the backslash character for it to render correctly, so typing `\\;` works correctly. See this: https://math.codidact.com/posts/278772#answer-278772 (more) |
— | over 3 years ago |
| Comment | Post #280462 |
+1 This is exactly what I needed, thank you for the clear explanation and the reference! :) (more) |
— | over 3 years ago |
| Comment | Post #280204 |
@msh210 I usually add the remainder of any proofs at the end of my questions (or I used to, on SE), but I somehow forgot to do so here. Thanks for asking about it! (more) |
— | over 3 years ago |
| Comment | Post #280204 |
@msh210 It goes like this: "Thus $$\mathcal{R}_p^{(\pi/2)} \circ \mathcal{R}_s^{(\pi/2)} = (\mathcal{R}_m^\pi)^{-1} \circ \mathcal{M} = \mathcal{R}_m^\pi.$$ If we define $s' = \mathcal{R}_m^\pi(s)$ then $m$ is the midpoint of $ss'$. But, on the other hand, $$s' = \Bigl( \mathcal{R}_p^{(\pi/2)} \circ ... (more) |
— | over 3 years ago |
| Comment | Post #280207 |
@MonicaCellio Ah, you're right, I didn't notice that. Not sure why that should be the case. The part that is not rendered in the latest revision (2020-12-31T07:17:38Z) happens to be rendered in the initial revision. The only thing different about it is that it uses "displayed math" (hence the double ... (more) |
— | over 3 years ago |
| Comment | Post #280206 |
Okay, now this is actually a bit embarrassing for me. I just had to turn the page and find out in Figure [15a] that the point $k$ is indeed the point you call $z$. So, if you'll excuse me, I shall go drown myself now. (more) |
— | over 3 years ago |
| Comment | Post #280206 |
+1 This makes perfect sense. If this is what the author also meant, then I'm not sure why he phrased it as $\mathcal{M}(k) = k$, though. (more) |
— | over 3 years ago |
| Comment | Post #278724 |
This is happening to me, too. The editor slows down tremendously and drafting moderately long posts becomes quite difficult. (more) |
— | over 3 years ago |
| Comment | Post #280118 |
@MonicaCellio I tried editing the tags on the post just now and was somehow able to create new tags! I'm not sure what went wrong for me earlier. Thank you for pinging, though. :-) (more) |
— | over 3 years ago |
| Comment | Post #280118 |
@PeterTaylor Yes, that's right. I included more than just that part in the quote because I felt that it provided context for what Lang is trying to convey; hopefully, it isn't too confusing! (more) |
— | over 3 years ago |
| Comment | Post #280134 |
@celtshk That actually sounds quite feasible, I'll support that! (more) |
— | over 3 years ago |
| Comment | Post #280118 |
@DerekElkins In my mind, I was thinking of a finite monoid (or group) $G$ whose elements are indexed as $\\{ x_1, \dotsc, x_n \\}$ and $I = \mathbb{N}$, $J = \\{ n + 1\\}$. But perhaps the notion of indexing already assumes a bijection, so taking $I = \mathbb{N}$ is improper? (more) |
— | over 3 years ago |
| Comment | Post #280118 |
I would have preferred to have some algebra-related tags on my question, but it seems that such tags don't already exist and I cannot create them. Could users with more privileges please help me choose a better set of tags? (more) |
— | over 3 years ago |
| Comment | Post #280064 |
A similar question asked on Mathematics Educators SE (sharing because there are some interesting answers there too): [How to justify teaching students to rationalize denominators?](https://matheducators.stackexchange.com/q/1860) (more) |
— | over 3 years ago |
| Comment | Post #280069 |
This is a really insightful answer! +1 (more) |
— | over 3 years ago |
| Comment | Post #278638 |
But, $x_{r-j}$ is *not* equal to $n^j x_r$! (I presume you meant modulo $10$?) For instance, for the decimal expansion of $1/19$, $x_{r-5} = 3$ but $2^5 x_r = 32 \neq 3 \pmod{10}$. In fact, they are not equal precisely because of the carrying-over happening in the concatenation process. I'm sorry, bu... (more) |
— | over 3 years ago |
| Comment | Post #278638 |
Secondly, though I say this "works", how do I adequately make sense of that? After all, the string that I get by my method of concatenation strictly speaking gives an "infinite number" such as $\dotsc 052631578947368421$. So perhaps, my claim is something like $$\frac{1}{10n-1} = \lim_{k \to \infty} ... (more) |
— | over 3 years ago |
| Comment | Post #278638 |
Thank you for your answer! I hope you won't mind if I say that I somehow feel this answer doesn't go all the way towards explaining why this "*backwards* concatenation" process appears. Specifically, I do understand that if $x = 0.\overline{x_1 x_2 x_3 \dotso x_r}$, then $x$ is a rational number equa... (more) |
— | over 3 years ago |