Activity for celtschk
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| 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) |
— | about 2 years ago |
| Edit | Post #287369 | Initial revision | — | about 2 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 the n... (more) |
— | about 2 years ago |
| Edit | Post #287361 | Initial revision | — | about 2 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 ordinal... (more) |
— | about 2 years ago |
| Edit | Post #287269 |
Post edited: Better name for the tag |
— | about 2 years ago |
| Edit | Post #287269 |
Post edited: Added a textual description of the formula |
— | about 2 years ago |
| Edit | Post #287269 |
Post edited: |
— | about 2 years ago |
| Edit | Post #287269 | Initial revision | — | about 2 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 gene... (more) |
— | about 2 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) |
— | about 2 years ago |
| Edit | Post #287192 | Initial revision | — | about 2 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 to ... (more) |
— | about 2 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 sure t... (more) |
— | over 2 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? 52431? S... (more) |
— | over 2 years ago |
| Comment | Post #286985 |
I think you mean $\frac\pi6$ instead of $\frac\pi3$. (more) |
— | over 2 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 need... (more) |
— | over 2 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 |
— | over 2 years ago |
| Edit | Post #286854 |
Post edited: fixed typo |
— | over 2 years ago |
| Edit | Post #286854 |
Post edited: Added example with image for clarity |
— | over 2 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) |
— | over 2 years ago |
| Edit | Post #286854 |
Post edited: Noted special case |
— | over 2 years ago |
| Edit | Post #286854 | Initial revision | — | over 2 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 unique fi... (more) |
— | over 2 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 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) |
— | over 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) |
— | almost 3 years ago |
| Edit | Post #285613 |
Post edited: Added MathJax source code as code block, and MathJax-rendering tag |
— | almost 3 years ago |
| Edit | Post #285614 | Initial revision | — | almost 3 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: $\begin{array} {|r|r|}\hline \text{If I already earned a} & \text{then I must roll another} \\\\ \hline 9 & 1 \\\\ \hline 8 & 2 ... (more) |
— | almost 3 years ago |
| Suggested Edit | Post #285613 |
Suggested edit: Added MathJax source code as code block, and MathJax-rendering tag (more) |
helpful | almost 3 years ago |
| Comment | Post #285596 |
The Markdown interpreter on StackExchange is sufficiently aware of MathJax syntax to avoid such things. QPixel's interpreter unfortunately isn't. The dollar sign is just one instance of that problem; also inside MathJax formulas, the backslash often needs to be doubled here.
See e.g. [here](https:... (more) |
— | almost 3 years ago |
| Edit | Post #285596 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Why doesn't \$ work? You need to use `\\$`, 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), with... (more) |
— | almost 3 years ago |
| Edit | Post #285526 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How's it possible to arrange 0 objects? How can 0! = 1? How is it possible to arrange $0$ objects? Well, by doing nothing. Doing nothing is something you can do, and you can do it in exactly one way. Another way to see it is to consider that it is also the number of ways you can rearrange the objects in a row. One way to rearrange the objects is, again... (more) |
— | almost 3 years ago |
| Edit | Post #285345 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Is Mathematical Induction truly "induction", or misnamed? In the context of Peano arithmetics, mathematical induction is actually an axiom, that is you cannot prove it from other properties of the natural numbers. It is extremely plausible that if something holds for $0$, and if it holds for $n$ it also holds for $n+1$, that it holds for all natural numbers... (more) |
— | about 3 years ago |
| Edit | Post #285327 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Why must percent change divide the difference by the old, NOT new, value? When you say “the value changed by 5%” what you actually mean is “the value changed by 5% of the old value” (this is by convention because that is in the vast majority of cases the quantity you are interested in). And that is why you have to divide the difference by the old value. If you want to b... (more) |
— | about 3 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) |
— | about 3 years ago |
| Edit | Post #284557 |
Post edited: |
— | about 3 years ago |
| Edit | Post #284557 | Initial revision | — | about 3 years ago |
| Question | — |
Does this construction always give a topological vector space? Consider an algebraic vector space $V$ over $\mathbb R$ or $\mathbb C$. Now for each possible basis $Bk = \\{ei^{(k)}|i\in I\\}$ of $V$, one can define an inner product $\langle\cdot\vert\cdot\ranglek$ by $\langle ei^{(k)}\vert ej^{(k)}\ranglek = \delta{ij}$ (for vector spaces of infinite dimensio... (more) |
— | about 3 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 3 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 3 years ago |
| Edit | Post #283889 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Getting backward of partial differentiation's chain rule Your main error is to treat the derivatives as fractions. From the definition, they are not fractions, they are limits of fractions. Now for total derivatives treating them like fractions generally gives correct results (at least I never have seen any case where it fails), therefore one might c... (more) |
— | over 3 years ago |
| Edit | Post #283619 | Initial revision | — | over 3 years ago |
| Question | — |
MathJax doesn't render after editing comment I've just noticed that when editing a comment with MathJax, the MathJax content is not rendered after finishing the edit. Note that after a page reload, it again renders correctly. (more) |
— | over 3 years ago |
- ← Previous
- 1
- 2
- 3
- 4
- Next →