Activity for celtschk
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #287846 |
Your (2') is never true, as $\emptyset\in\mathscr B$, but there certainly doesn't exist a nonempty $B'\subset\emptyset$. In (2) the empty set is excluded by the demand that $x\in\mathscr B$. You need to explicitly exclude $B$ from being the empty set in order for (2') to be possibly true. (more) |
— | about 1 year ago |
| Comment | Post #287764 |
On reputation not limiting your actions: It is an intentional design. Codidact *does* limit your abilities, but it doesn't do so on reputation, but on measures that relate to the abilities. For example, you cannot gain edit ability by answering many questions, but by suggesting many edits that got ac... (more) |
— | over 1 year ago |
| Comment | Post #287764 |
While I agree it would make sense to separate the two, note that having a high reputation on Q&A doesn't imply you're a good mathematician either. You may gather reputation by simply asking many good questions. Or you may gather upvotes by giving good pedagogical answers to simple mathematical questi... (more) |
— | over 1 year ago |
| Comment | Post #287518 |
I don't think it's technically possible to block display math on parts of a page (but I might be wrong on this). But maybe submitting a title with it can be blocked. (more) |
— | over 1 year ago |
| Comment | Post #287419 |
@#53407 Well, the “length” is defined in the title as the number of the points that come to lie on the perimeter of the convex hull. It's not what conventionally would be called “length” (yes, it's another case of confusing wording, but in this case the exact intended definition is contained in the q... (more) |
— | over 1 year ago |
| Comment | Post #287419 |
I see, so you should simply remove the word "grid" to make your question vastly more understandable. You have a square with randomly distributed points in it. No grid that is of any relevance. (more) |
— | over 1 year ago |
| Comment | Post #287410 |
The product as you've written it now is not well defined, and I think not what you wanted anyway. It is an infinite product. (more) |
— | over 1 year ago |
| Comment | Post #287419 |
So what is the point of the grid in the first place? (more) |
— | over 1 year ago |
| Comment | Post #287419 |
Err, actually even in the case of identical points we have $l=4$ for all configurations, as the identical points still need to be counted separately. But still a counterexample. (more) |
— | over 1 year ago |
| Comment | Post #287419 |
Actually thinking about it, it's a counterexample in the other case, too, as there are more configurations with two points identical than all points different. (more) |
— | over 1 year ago |
| Comment | Post #287419 |
Are two points allowed to be identical? Otherwise the case of four points on a 2×2 grid is an obvious counterexample, as the probability of $l=3$ is 0, and of $l=4$ is 1. (more) |
— | over 1 year ago |
| Comment | Post #287178 |
$K_1$ and $K_2$ are just arbitrary names for constants. If you prefer, you can name those constants $C_1$ and $C_2$. Or $s$ and $m$ because you have to **s**ubtract one, and to **m**ultiply by the other. The names don't matter, just how you calculate them. (more) |
— | over 1 year ago |
| Comment | Post #286991 |
Well, the second spot is already occupied, so you have to decide what to do with the book that's already there. From the example, I conclude that you move the book and those in between that spot and the original spot of the picked book one position towards that original spot, right?
To make sure t... (more) |
— | over 1 year ago |
| Comment | Post #286991 |
What happens with the other books when you put a book in the right spot? Do you exchange the book with the other one? Or do you move all books in between one spot to the left/right?
For example, if your current order is 54321, and you pick book 2, what will the order be afterwards? 52341? 52431? S... (more) |
— | over 1 year ago |
| Comment | Post #286985 |
I think you mean $\frac\pi6$ instead of $\frac\pi3$. (more) |
— | over 1 year ago |
| Comment | Post #286908 |
@#53398 “The usual way for defining $a^x$ for arbitrary real $x$ is via $e^{x\ln a}$” — Is that really the *usual* way? The definition I know is that you start with the definition for rational $x$ and define the value for irrational $x$ through continuity. Of course then to define $e^x$ you also need... (more) |
— | over 1 year ago |
| Comment | Post #286854 |
You seem to have missed the bit about the integer grid.
I've now added an example with image to make it more clear. (more) |
— | over 1 year ago |
| Comment | Post #286572 |
Could you please add the definition of an entropic structure? I can't find it in a web search, and I don't have access to that book.
(more) |
— | almost 2 years ago |
| Comment | Post #286453 |
@Peter Taylor: If I interpret everything correctly, you should have: $D_xg^{-\epsilon} = (-\epsilon)g^{-\epsilon-1}g'$. Note the explicit minus sign in front of the prefactor. (more) |
— | almost 2 years ago |
| Comment | Post #285723 |
Actually for $\sqrt{18}$ it's even easier to see: Obviously $\sqrt{18} > \sqrt{16} = 4$, and clearly a larger square does not fit into a smaller square, regardless of any grid.
(more) |
— | over 2 years ago |
| Comment | Post #285596 |
The Markdown interpreter on StackExchange is sufficiently aware of MathJax syntax to avoid such things. QPixel's interpreter unfortunately isn't. The dollar sign is just one instance of that problem; also inside MathJax formulas, the backslash often needs to be doubled here.
See e.g. [here](https:... (more) |
— | over 2 years ago |
| Comment | Post #284788 |
Topology is a vast field. Asking whether you should learn it is like asking whether you should learn set theory. You certainly should know the fundamentals (such as, what is a neighbourhood, or what is a continuous function), and anything related to other theories you are interested in, but there's a... (more) |
— | over 2 years ago |
| Comment | Post #284113 |
It is not true that for differentiating you simply “increase dot”. Rather, you apply the differentiation rules. Having said that, while taking the derivative usually can be done quite mechanically, integration cannot be done that way (well, technically it can, but the algorithm is so complicated that... (more) |
— | over 2 years ago |
| Comment | Post #283947 |
Just a note: Depending on the programming language, also in programming the subexpressions may be evaluated in any order. This is why e.g. in C and C++, expressions like `i+(i++)` are undefined behaviour. (more) |
— | over 2 years ago |
| Comment | Post #283593 |
@#53922 Yes, you understand continuous wrong. Continuity does *not* mean that the graph is path connected. Continuity means that you get arbitrary small changes of $f(x)$ for sufficiently small changes of $x$ *inside the domain.* The following would be a discontinuous function:
$$f(x) = \begin{cases... (more) |
— | over 2 years ago |
| Comment | Post #283390 |
I personally learned GR, including the involved mathematics, from the book *Gravitation* by Misner, Thorne and Wheeler. However that's not a math book, therefore if you want mathematical rigour, that book likely isn't for you (e.g. IIRC you won't find any proofs there). Other than that I don't have s... (more) |
— | over 2 years ago |
| Comment | Post #283390 |
I haven't looked into the book (therefore only a comment), but while the topics listed in the title are relevant for quantum theory, they are generally irrelevant or at most tangentially relevant for General Relativity. Therefore I suspect that it is not the best book if your goal is to understand G... (more) |
— | over 2 years ago |
| Comment | Post #283332 |
In your perimeter example, some of the squares the circle crosses are not black; in other words, the pixels do not *cover* the circle. Otherwise you'd get a better approximation. Indeed, the Hausdorff measure is exactly defined by such coverings.
In particular, in your 1st grid, you've got 8 cover... (more) |
— | over 2 years ago |
| Comment | Post #283111 |
This isn't a question about mathematics, but about the specific language used in medicine (I'm not aware of those two terms being used outside that context). It possibly would be on-topic on a medicine site (which Codidact currently doesn't have AFAICT), but not here. It *might* me on-topic on Langua... (more) |
— | over 2 years ago |
| Comment | Post #283154 |
Please see the edit, I hope it clears things up. (more) |
— | over 2 years ago |
| Comment | Post #283197 |
Yes, now I get the edit window, so that issue seems to be fixed. Thank you. (more) |
— | over 2 years ago |
| Comment | Post #283154 |
Yes, it's a square, with side length (of each of its four sides) $\sqrt{50}$. I tried to add an explanation to the answer, but at the moment for some reason I can't edit it (I've posted a bug report on meta on this). (more) |
— | over 2 years ago |
| Comment | Post #283154 |
But the side length of the sketched square is not $5$, but $\sqrt{50}$. (more) |
— | over 2 years ago |
| Comment | Post #283087 |
Note that the fact that your result passes that test is not a proof that your result is correct, just that you cannot prove it incorrect that way (and indeed, no different power of $x$ would be correct).
On the $x$ in the numerator and denominator: You mentioned as one difference between your resu... (more) |
— | almost 3 years ago |
| Comment | Post #283087 |
Dimensional analysis is a quick check normally done on physics equations: If the equation is correct, all terms must have the correct units. Now while your equation for $I$ (probably) didn't come from a physics problem, one can pretend that it does, with $x$ having an arbitrary unit (that would depen... (more) |
— | almost 3 years ago |
| Comment | Post #282343 |
Unless I've missed something, all MathJax I could see on the page (including that in comments) renders fine for me (Waterfox Classic/Linux). (more) |
— | almost 3 years ago |
| Comment | Post #281203 |
Thank you for your answer (and sorry for my late reaction). Indeed I was after the space spanned by finite linear combinations of the $\omega_i$; I thought (incorrectly, as I now see) that I had found a base-independent characterisation, which would have meant that it is base independent. So IIUC, th... (more) |
— | almost 3 years ago |
| Comment | Post #280654 |
Thank you. I did know the term embedding for Riemannian manifolds, but wasn't aware of the purely topological usage. Stated that way, the relation looks natural enough that someone ought to have thought of it before. (more) |
— | about 3 years ago |
| Comment | Post #280340 |
Maybe it would be a good idea to make the autosave interval configurable (ideally per community, or simply two settings depending on whether MathJax is enabled or disabled). An autosave every five minutes would still be quite useful, but probably not too disruptive even with MathJax rendering. (more) |
— | over 3 years ago |
| Comment | Post #280462 |
I think in the presence of a crosscap, each handle should be convertible to two crosscaps, therefore $g$ handles and $k$ crosscaps with $k\ge 1$ should be equivalent to $2g+k$ crosscaps. But I'm not entirely sure. (more) |
— | over 3 years ago |
| Comment | Post #280068 |
@tommi: One case where the $1/\sqrt{3}$ definitely is more useful is as coefficient in a quantum state: You see immediately that the absolute square (which gives the corresponding probability) is $1/3$, which for $\sqrt{3}/3$ takes more cognitive load to see. Therefore which convention is more useful... (more) |
— | over 3 years ago |
| Comment | Post #280134 |
On the duplication issue: Maybe one could make a FAQ category populated with curated answers to popular questions. The FAQ would initially be populated by questions crafted on frequent questions on Math SE, and later extended to cover questions that turn out to be asked frequently here. This could be... (more) |
— | over 3 years ago |
| Comment | Post #280133 |
I think the first thing that has to be addressed is the bad interaction between MarkDown and MathJax on this site (the backslash problem). See [here](https://math.codidact.com/posts/278763) for details. I have some ideas on how this might be addressed on an algorithmic level, but unfortunately I have... (more) |
— | over 3 years ago |
| Comment | Post #280127 |
@luap42: Thank you; you're quick! (more) |
— | over 3 years ago |
| Comment | Post #280068 |
@tommy: That assumes that the numerical value is what you are interested in. Which is sometimes the case, but certainly not always. (more) |
— | over 3 years ago |
| Comment | Post #280069 |
Note that your third "we want" point is a direct consequence of the first two. Anyway, great answer, +1. (more) |
— | over 3 years ago |
| Comment | Post #279400 |
I have trouble to figure out what your intuition actually is. What is the unit of the denominator $2$ in "half a cake"? Anyway, the $1$ has to be dimensionless (having no unit) for the formula to work. It just means the number one. (more) |
— | over 3 years ago |
| Comment | Post #279026 |
@msh: I've now looked up the small inductive dimension, and I don't think it fits. In particular, the point types in general are only partially ordered, while the small inductive dimensions are by construction totally ordered. Also, if you equip a von-Neumann ordinal $\alpha$ with the topology $\alph... (more) |
— | over 3 years ago |
| Comment | Post #278772 |
One possibility to fix this is before passing it to MarkDown to pass it through another code which escapes all backslashes occurring inside MathJax expressions. That code would only have to detect the configured MathJax triggers (i.e. the dollar signs, and whatever else MathJax is configured to inter... (more) |
— | over 3 years ago |
| Comment | Post #278724 |
Happens also for me with Waterfox Classic on Linux. In particular the re-rendering on moving the cursor is annoying; a re-rendering should only be triggered when the edited content actually changes. (more) |
— | over 3 years ago |