Activity for celtschk
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #287880 |
Post edited: Removed further application because I now think I got it wrong |
— | about 1 year ago |
| Edit | Post #287880 | Initial revision | — | about 1 year ago |
| Question | — |
Unification and generalization of limit and colimit The recent post by r reminded me of my own idea to unify and generalise limit and colimit. I also only occasionally dabble in category theory, and thus I wonder if the following is a sound construction, and if so, if it is a known concept. The idea is as follows: We have a category $\mat... (more) |
— | about 1 year ago |
| Edit | Post #287848 |
Post edited: fixed some grammar errors |
— | about 1 year ago |
| Edit | Post #287848 |
Post edited: fixed typo |
— | about 1 year ago |
| Edit | Post #287848 | Initial revision | — | about 1 year ago |
| Answer | — |
A: Criterion in terms of the bases for determining whether one topology is finer than another A counterexample would be the set $S=\{0,1,2\}$ with the topologies $\mathcal T = \{\emptyset, \{0\}, \{0,1\}, S\}$and $\mathcal T' = \{\emptyset,\{0\},S\}$. Clearly $\mathcal T'$ is not finer than $\mathcal T$. Now $\mathcal T$ is generated by the basis $\mathscr B = \{\{0\},\{0,1\},S\}$ and $\ma... (more) |
— | about 1 year ago |
| 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) |
— | about 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 |
| Edit | Post #287724 | Initial revision | — | over 1 year 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 exis... (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 |
| Edit | Post #287410 |
Post edited: Changed displaymath to inline math in title |
— | over 1 year ago |
| Suggested Edit | Post #287410 |
Suggested edit: Changed displaymath to inline math in title (more) |
helpful | over 1 year ago |
| Edit | Post #287481 | Initial revision | — | over 1 year 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 preview c... (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 |
| Edit | Post #287369 | Initial revision | — | over 1 year 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 the n... (more) |
— | over 1 year ago |
| Edit | Post #287361 | Initial revision | — | over 1 year 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 ordinal... (more) |
— | over 1 year ago |
| Edit | Post #287269 |
Post edited: Better name for the tag |
— | over 1 year ago |
| Edit | Post #287269 |
Post edited: Added a textual description of the formula |
— | over 1 year ago |
| Edit | Post #287269 |
Post edited: |
— | over 1 year ago |
| Edit | Post #287269 | Initial revision | — | over 1 year 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 gene... (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 |
| Edit | Post #287192 | Initial revision | — | over 1 year 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 to ... (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 |
| 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 |
— | over 1 year ago |
| Edit | Post #286854 |
Post edited: fixed typo |
— | over 1 year ago |
| Edit | Post #286854 |
Post edited: Added example with image for clarity |
— | 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 |
| Edit | Post #286854 |
Post edited: Noted special case |
— | over 1 year ago |
| Edit | Post #286854 | Initial revision | — | over 1 year 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 unique fi... (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) |
— | about 2 years ago |