Activity for Peter Taylor
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #291301 |
For the purposes of "each point in $X$ is in the image of exactly one such restriction $\sigma_\alpha | \overset{\circ}{\Delta}{}^n$" does the 0-simplex count as having a non-empty interior? If not, the points mapped by the vertex would seem to be exceptions. (more) |
— | 11 days ago |
| Comment | Post #291104 |
I haven't worked through it, but my first thought is that your diagram doesn't seem to use any properties of the circumcircle. I wonder whether the fact that the perpendicular bisector of CD is parallel to MD and passes through the centre of the circle will be relevant. (more) |
— | about 1 month ago |
| Comment | Post #290814 |
The FAQ says "Don't cross-post the same thing in multiple topics". I believe that "topics" is a term which generalises "question" to cover sites which have blog posts, articles, etc. Cross-posting questions across sites / networks without mentioning it is poor netiquette, but here the OP did provide ... (more) |
— | about 2 months ago |
| Comment | Post #290894 |
Yes, you're right. I don't think I've kept all of my previous Sage code so I can't try to figure out where I made the mistake, but that does open up some other ideas for extensions to $6 \times 6$. (more) |
— | about 2 months ago |
| Comment | Post #290894 |
This can be rephrased as $$(A+I)^{-1} = \frac{(1 + a_{01}^2 + a_{02}^2 + a_{12}^2)I - A + A^2}{|A+I|}$$ where $|A+I| = 1 + a_{01}^2 + a_{02}^2 + a_{12}^2$. For $4\times 4$ and $5\times 5$ it generalises respectively to $$-\frac{(1 + a_{01}^2 + a_{02}^2 + a_{03}^2 + a_{12}^2 + a_{13}^2 + a_{23}^2)(A -... (more) |
— | 2 months ago |
| Comment | Post #290864 |
If you want to learn advanced mathematics, the best route is to work through a textbook. If you come to a proof that you can't understand, feel free to ask a specific question about that proof. Wikipedia mathematics pages are often more helpful as a refresher on something already studied than as a re... (more) |
— | 2 months ago |
| Comment | Post #290581 |
The case analysis needs to take into account the possibility of a 2-2-0-0 split. If there are 4 voters and 4 candidates then there are $4^4 = 64$ ways for them to vote. (more) |
— | 3 months ago |
| Comment | Post #290025 |
More generally, when $n > m$ the sum has no support so the LHS is zero. (more) |
— | 6 months ago |
| Comment | Post #289814 |
The page you link for tau-distribution says (variables adjusted for consistency with your presentation) "In fact, this implies that $\frac{\tau_\nu^2}{\nu}$ follows the beta distribution $B(\frac12,\frac{ν − 1}2)$." Is that effectively an answer? Stats was never my strongest subject and I'm very rust... (more) |
— | 7 months ago |
| Comment | Post #289757 |
I'm not sure why it's relevant that they're 16-year-olds, and that prompts me to consider that this is really a question for teachers about pedagogy rather than for mathematicians about mathematics, so this may not be the right place to ask. I've raised the scope question [on meta](https://math.codid... (more) |
— | 7 months ago |
| Comment | Post #289760 |
If you think the previous question needs improving, edit the previous question rather than duplicating it with minor tweaks. (more) |
— | 7 months ago |
| Comment | Post #289671 |
Firstly, it wasn't my edit. I don't understand why you call it my edit after having described the situation accurately in the question. Secondly, I understood the question to be about the edit summary. If that wasn't the main point, I suggest either editing the question or asking a new one. Thirdly, ... (more) |
— | 8 months ago |
| Comment | Post #289671 |
I wanted to approve the edit but change the edit summary to remove the mention of correctness, but this option wasn't available. (more) |
— | 8 months ago |
| Comment | Post #289216 |
What exactly do you mean by "real infinite series"? Without the surrounding context I would interpret it as a function $\mathbb{N} \to \mathbb{R}$, but that can't be involutory unless it's an infinite series of natural numbers, in which case specifying "real" makes no sense. Are you looking for analy... (more) |
— | 9 months ago |
| Comment | Post #289012 |
Maybe someone with more imagination than me can see a way, but I'm not. (more) |
— | 9 months ago |
| Comment | Post #289012 |
The question "But why do most answers on lotteries consider the Pr(winning jackpot in 1 play)" might be on-topic as a *meta* question, but the answer is going to be along the lines of "Because that's what the questions ask about". As to *Homo economicus*, this is a mathematics site, and while tightly... (more) |
— | 9 months ago |
| Comment | Post #288820 |
Yes. Consider a 3x3 grid with mines at (0,1), (1,0), (1,1) and an initial clue at (2,2). (more) |
— | 10 months ago |
| Comment | Post #288729 |
I assume that the values are integers. What are the default values and the supported bounds? (more) |
— | 10 months ago |
| Comment | Post #287787 |
I think you've missed the "(End)". The paragraph about 49 is part of [Schoenfield's original submission](https://oeis.org/history/view?seq=A309981&v=3). (more) |
— | 10 months ago |
| Comment | Post #288113 |
The first question is borderline mathematical. The second question is not, so I'm going to edit to remove it. (more) |
— | 12 months ago |
| Comment | Post #288022 |
I haven't analysed it in detail, but I don't think that *a priori* it can be assumed to be fallacious. (more) |
— | about 1 year ago |
| Comment | Post #288022 |
It's not impossible in principle to make a profit by buying every number combination, although it requires a large syndicate both to invest and to obtain the tickets; a lottery where unwon prizes roll over so that the jackpot gets large enough to be worth it; and a bit of luck so that you're not shar... (more) |
— | about 1 year ago |
| Comment | Post #287999 |
I was specifically assuming that the numbers on each ticket are *not* randomly generated but chosen by the player. (more) |
— | about 1 year ago |
| Comment | Post #287999 |
I would say that in the context of the question the chance of winning is linear with the number of tickets because we can assume that the tickets will not have the same numbers, and a perfect match with the selected numbers is required to win, so they cover different outcomes of a single event. (more) |
— | about 1 year ago |
| Comment | Post #287958 |
To properly answer this question we would need full details on the prize structure (because most lotteries have more than just the top prize) and sufficient details on the ticket structure to estimate the chances of prizes being shared. (more) |
— | about 1 year ago |
| Comment | Post #287787 |
Certainly $p_0 \in$ [A183064](https://oeis.org/A183064) shows that candidates are quite sparse. (more) |
— | about 1 year ago |
| Comment | Post #287764 |
I think that it's intended to be seen as community reputation rather than mathematics reputation: it measures your contribution to the math.codidact.com community (and that, in turn, is arguably a proxy for activity in the math.codidact.com community, as long as you're not mainly making posts which g... (more) |
— | over 1 year ago |
| Comment | Post #287761 |
Your comment about the unapproved edit possibly points to the need for a feature request. I'm a site moderator but the moderation tools don't seem to show a queue of edits pending approval. If it's still pending, post a link in this comment thread and I'll look at it. (more) |
— | over 1 year ago |
| Comment | Post #287674 |
The choice of symbols is separate to the choice of base. The symbols which you call Arabic numerals in the question aren't the 10 symbols used in Arabic. Computer programmers tend to use 0123456789abcdef for hexadecimal. But it seems to me that the choice of symbols is a question of communication as ... (more) |
— | over 1 year ago |
| Comment | Post #287674 |
Is this a question about mathematics? (more) |
— | over 1 year ago |
| Comment | Post #287588 |
[Quadratic programming](https://en.wikipedia.org/wiki/Quadratic_programming) has a long Wikipedia page which I won't attempt to summarise beyond to say that it's about optimising an "objective function" subject to quadratic constraints. Since all you care about is the existence of a solution, the cho... (more) |
— | over 1 year ago |
| Comment | Post #287588 |
"Correct assignment of signs": when I said "signed volume" it's because if the given value is negative you need to negate it to get the correct volume. Assigning the signs is essentially guessing which ones need to be negated. (The last sentence gives an idea for making an intelligent guess; in the w... (more) |
— | over 1 year ago |
| Comment | Post #287518 |
I think it would be possible to replace `$$` with `$`, similarly with whatever other block markers are configured, and `\begin` with `%` or something else which makes the eqnarray or cases or whatever environment obviously not render so that the poster realises there's something to fix. (more) |
— | over 1 year ago |
| Comment | Post #287481 |
View Source shows that the raw HTML being sent to the browser is `A parabola is given by $y^2=2px$ with $p>0$. The point $D$ is on the parabola in the first quadrant at a distance of $8$ from the $x$-a...` so the problem is a double-escaping. (more) |
— | over 1 year ago |
| Comment | Post #287492 |
Rather than mapping the whole original example, maybe you can split it: at least one of the ranges $[0, 1]$ and $[1, \infty)$ must preserve the property, and if it's the latter then it's at least worth considering that it still preserves the property under the mapping $x \to \frac1x$. (more) |
— | over 1 year ago |
| Comment | Post #287178 |
@#55348, if you take any 2D shape with a well-defined area and sweep it along its normal to create a generalised prism of height h, the volume will be the area times h. If you linearly scale the shape by the same scale in both directions, the area of the shape (and hence the volume of the generalised... (more) |
— | over 1 year ago |
| Comment | Post #286991 |
I've seen this problem before, I but can't remember the details. One thing which does stand out is that the extrema settle. If you consider e.g. ordering $1,2,5,3,4,6$, the $1,2,\ldots$ and $\ldots,6$ are now fixed. (more) |
— | over 1 year ago |
| Comment | Post #286854 |
Ok, I get it now. For some reason I was visualising the spiral as going inwards, not outwards. (more) |
— | over 1 year ago |
| Comment | Post #286854 |
This isn't bijective: it doesn't encode information about the width and height of the spiral, so it can't be decoded. (more) |
— | over 1 year ago |
| Comment | Post #286709 |
I wonder whether the textbook was badly translated into English. A more standard name for $m_1, m_2, \ldots, m_k$ would be *intermediate terms*, and you'll probably find that more useful for communicating with people who didn't use the same textbook. (more) |
— | almost 2 years ago |
| Comment | Post #286709 |
Are you sure that "mean" is the correct word? The arithmetic mean of a collection of numbers is the most common form of average. I would guess from the example that the term you want is "number of intermediate values", but I'm not certain that it's the only possibility. (more) |
— | almost 2 years ago |
| Comment | Post #286569 |
I tried two cost functions for "even spacing". If the *gap* between two consecutive values is the difference of their logarithms, the first cost function was the difference between the largest gap and the smallest gap; and the second cost function was the variance of all the gaps. I can't tell you of... (more) |
— | almost 2 years ago |
| Comment | Post #286572 |
I don't know and right now can't see the answer, but the obvious point (which has probably already occurred to you but which I make for completeness) is that you don't seem to have used the precondition "$\alpha \odot \beta$ is the identity automorphism". (more) |
— | almost 2 years ago |
| Comment | Post #286453 |
I can't see where the conclusion $D_x g^{-\epsilon} < 0$ comes from. $\epsilon > 0$, $g^{1+e}(x) > 0$, $g'(x) > 0$, so it seems to me that $D_x g^{-\epsilon} > 0$. (more) |
— | almost 2 years ago |
| Comment | Post #286472 |
Two things. 1. For consistency with the other tags on the site, please use lower case unless there's a good reason not to (e.g. people's names, standard upper-case symbols). 2. What is "numerical" intended to capture? Numerical analysis? (more) |
— | almost 2 years ago |
| Comment | Post #286034 |
@#53398, I'm not sure I get it either. If we have a rotation in a plane around the origin which, applied twice, takes us from $(1,0,0)$ to $(-1,0,0)$ then the plane must contain the origin, the start point, and the end point. By symmetry the square roots of $-1$ end up all being in the plane through ... (more) |
— | almost 2 years ago |
| Comment | Post #286188 |
On the subject of having no idea how to answer a question, it's always a good starting point to write it out in terms of the definitions. So "the expected time until the buffer reaches its capacity for the first time" is a weighted sum of probabilities, and the question largely reduces to calculating... (more) |
— | about 2 years ago |
| Comment | Post #286188 |
This site uses a markup tool called MathJax which would improve the legibility of your question considerably. If you surround each formula/expression with dollar signs, you can use underscores `_` to create subscripts, carets `^` to create superscripts, curly brackets `{}` to group subscripts or supe... (more) |
— | about 2 years ago |
| Comment | Post #286166 |
Rather than thinking about going "out of 3D space", it may be helpful to think about it as working with the surface of a 3D unit hypersphere embedded in a 4D space. (more) |
— | about 2 years ago |
| Comment | Post #286004 |
Which skewness and which sample skewness? There seem to be multiple, subtly different, parameters with those names. (more) |
— | about 2 years ago |