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) |
— | over 3 years 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 go... (more) |
— | over 3 years 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 qu... (more) |
— | over 3 years ago |
| Edit | Post #287724 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Proving $|{\bf R}^{\bf R}|=|2^{\bf R}|$ using the Schroeder-Bernstein Theorem To apply the Schröder-Bernstein theorem, we need injections in two directions. Given that the Schröder-Bernstein theorem doesn't require the axiom of choice (AC), there's a value in avoiding anything that requires AC (such as the theorem that existence of a surjection from $A$ to $B$ implies the ... (more) |
— | over 3 years 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) |
— | almost 4 years ago |
| Edit | Post #287410 |
Post edited: Changed displaymath to inline math in title |
— | almost 4 years ago |
| Suggested Edit | Post #287410 |
Suggested edit: Changed displaymath to inline math in title (more) |
helpful | almost 4 years ago |
| Edit | Post #287481 | Initial revision | — | almost 4 years ago |
| Question | — |
LaTeX formulas not rendered correctly in summary I've noticed that the question preview of several questions on the Q&A page contains “misplaced &” with yellow background, which turns out to be a MathJax error. However opening one of them shows that the post itself is just fine. However the formula that doesn't correctly show up in the previ... (more) |
— | almost 4 years 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 t... (more) |
— | almost 4 years 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) |
— | almost 4 years 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) |
— | almost 4 years ago |
| Comment | Post #287419 |
So what is the point of the grid in the first place? (more) |
— | almost 4 years 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) |
— | almost 4 years 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) |
— | almost 4 years 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) |
— | almost 4 years ago |
| Edit | Post #287369 | Initial revision | — | almost 4 years ago |
| Question | — |
How to get rid of the tag ordinals? On my latest question, which was about ordinal numbers (often just called ordinals), I originally used the new tag ordinals. Later I noticed that ordinal-numbers would be a much better name for that tag. Since my question was still the only one using the tag, I simply retagged it, assuming that t... (more) |
— | almost 4 years ago |
| Edit | Post #287361 | Initial revision | — | almost 4 years ago |
| Answer | — |
A: Is this formula for the minimal sum correct? I think I've solved the problem: The formula is correct. For the proof I'm using the decomposition $\alpha = \lambda + m$ and $\beta = \mu + n$ from the question. Also, I'll use the notation $A\cong B$ for “$A$ is order-equivalent to $B$”. Also note that $+$ and $\cdot$ denote the standard ord... (more) |
— | almost 4 years ago |
| Edit | Post #287269 |
Post edited: Better name for the tag |
— | almost 4 years ago |
| Edit | Post #287269 |
Post edited: Added a textual description of the formula |
— | almost 4 years ago |
| Edit | Post #287269 |
Post edited: |
— | almost 4 years ago |
| Edit | Post #287269 | Initial revision | — | almost 4 years ago |
| Question | — |
Is this formula for the minimal sum correct? As is well known, the addition of natural numbers can be extended to the ordinal numbers in different ways. The first way is the ordinal sum, and the second is the natural or Hessenberg sum. Now I've been thinking about other possible sums of ordinals. For that purpose I've used the following ... (more) |
— | almost 4 years 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) |
— | almost 4 years ago |
| Edit | Post #287192 | Initial revision | — | almost 4 years ago |
| Question | — |
Does there exist a non-zero game such that the sum of three or more copies of it is zero? In combinatorial game theory, there are non-zero games $G$ with the property $G+G=0$; this is in particular true for all impartial games. Now I wonder if there also exist non-zero games such that $G+G+G=0$. I don't see an obvious reason why those shouldn't exist, but I also have no idea on how... (more) |
— | almost 4 years 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 su... (more) |
— | about 4 years 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? 5243... (more) |
— | about 4 years ago |
| Comment | Post #286985 |
I think you mean $\frac\pi6$ instead of $\frac\pi3$. (more) |
— | about 4 years 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 ... (more) |
— | about 4 years ago |
| Edit | Post #286854 |
Post edited: I noticed that with my example in between, it wasn't cear where the example ended; so I moved the example to the end and wen't completely through the procedure with it |
— | about 4 years ago |
| Edit | Post #286854 |
Post edited: fixed typo |
— | about 4 years ago |
| Edit | Post #286854 |
Post edited: Added example with image for clarity |
— | about 4 years 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) |
— | about 4 years ago |
| Edit | Post #286854 |
Post edited: Noted special case |
— | about 4 years ago |
| Edit | Post #286854 | Initial revision | — | about 4 years ago |
| Answer | — |
A: Is there a way to encode a unique arrangement of vertices of a graph with a unique short word? I'm going to assume your points are lying on an integer grid. I'm also assuming you always have a finite number of points. Then one way to make words for your point clouds is to enumerate the grid points, for example by starting at the origin and going in a spiral. Then you can assign an uniqu... (more) |
— | about 4 years 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) |
— | over 4 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) |
— | over 4 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 4 years ago |
| Edit | Post #285613 |
Post edited: Added MathJax source code as code block, and MathJax-rendering tag |
— | over 4 years ago |
| Edit | Post #285614 | Initial revision | — | over 4 years ago |
| Answer | — |
A: Why isn't MathJax table appearing? This is another instance of the general MathJax/Markdown problem noted here. If you replace all double backslashes (`\\`) with quadruple backslashes (`\\\\`), it works: $\begin{array} {|r|r|}\hline \text{If I already earned a} & \text{then I must roll another} \\\\ \hline 9 & 1 \\\\ \hline 8 ... (more) |
— | over 4 years ago |
| Suggested Edit | Post #285613 |
Suggested edit: Added MathJax source code as code block, and MathJax-rendering tag (more) |
helpful | over 4 years ago |
| Comment | Post #285596 |
The Markdown interpreter on StackExchange is sufficiently aware of MathJax syntax to avoid such things. QPixel's interpreter unfortunately isn't. The dollar sign is just one instance of that problem; also inside MathJax formulas, the backslash often needs to be doubled here.
See e.g. [here](ht... (more) |
— | over 4 years ago |
| Edit | Post #285596 | Initial revision | — | over 4 years ago |
| Answer | — |
A: Why doesn't \$ work? You need to use `\\$`, like this: \\$1. The reason is that MathJax is interpreted in the browser, while Markdown is interpreted in the server. If you write `\$`, then Markdown sees the backslash and therefore puts the dollar sign literally into the output (which it would have done anyway), ... (more) |
— | over 4 years ago |
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