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Activity for Peter Taylor‭

Type On... Excerpt Status Date
Comment Post #285086 I don't think that MCD is "based on" either site, but my point is that its scope is similar to MSE's and so it's not a surprise that it has the same problems as MSE.
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4 days ago
Edit Post #285086 Initial revision 5 days ago
Answer A: How can we grow this community?
Certainly low quality content is an issue. Being brutally honest, if I understood the rôle of moderator as being a ruthless dictator who pursues quality above all else I would delete 95% of the questions. But to put that in context, it's also true for most maths fora. I recently saw someone mention a...
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5 days ago
Comment Post #284996 That graphic helps a lot, thanks. But if the two initial squares aren't horizontally or vertically adjacent, it's not clear that the border is well defined. You can draw the 8-square box around each one, and then connect appropriate corners of the boxes with straight lines, but deciding which squares...
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6 days ago
Comment Post #284996 The notation can be read "the set of points $(0, t)$ where the variable $t$ is between $0$ and $1$ inclusive". It's just the line segment (technically not a line, because lines are infinite) between the two points.
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8 days ago
Comment Post #284996 This seems to be getting less clear, not more. Take a concrete example: let the two points be $(0, 0)$ and $(0, 1)$. What is the "minimal border" if not the line segment $\\{(0, t) \mid 0 \le t \le 1\\}$?
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8 days ago
Comment Post #285015 Turn the question around: what is *unintuitive* about it?
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9 days ago
Edit Post #285016 Post edited:
9 days ago
Edit Post #285016 Post edited:
9 days ago
Edit Post #285016 Initial revision 9 days ago
Answer A: How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)).
1. The two questions were closed as unclear because they're unclear. There's no dissimulation involved. 2. I don't see any evidence in r's comment that they understood the question. They say that you've ignored suggestions elsewhere for how to improve it, and they reference the introduction, but t...
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9 days ago
Comment Post #284996 The area of a circle is $\pi r^2$, and a point is the limit of a circle as $r \to 0$.
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11 days ago
Comment Post #285005 If the question is "Why does dividing two equal things by the same thing give two equal things" then I'm not sure why that isn't intuitive already. Separately, the first image gives a false statement (because you always need to be wary of the special case of division by zero), and I'm not sure what t...
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11 days ago
Edit Post #285005 Question closed 11 days ago
Comment Post #284997 I can't even guess at what you're asking.
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11 days ago
Edit Post #284997 Question closed 11 days ago
Edit Post #284788 Question closed about 1 month ago
Comment Post #284773 @#54114, when r~~ gave essentially the same answer in comments saying that it wasn't clear whether it was what you were looking for, your response was much more lukewarm.
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about 1 month ago
Edit Post #284550 Post edited:
about 1 month ago
Edit Post #282737 Post edited:
about 1 month ago
Comment Post #284550 Is "transpose matrix" a technical term from some field (perhaps mathematical physics) or should the tag be changed to `matrix-transpose`?
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about 1 month ago
Edit Post #284561 Post edited:
Remove tags which don't seem likely to fit many questions and create one which does
about 1 month ago
Comment Post #284561 If you're asking about notations that physicists use, you might have a better chance of getting a good answer on the physics site.
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about 1 month ago
Edit Post #284712 Post edited:
about 1 month ago
Edit Post #284712 Post edited:
about 1 month ago
Edit Post #284712 Initial revision about 1 month ago
Answer A: ratio of partial sums of the same geometric sequence
I think your approach is the expected one, but a shortcut if rigour is not required would be to note that the absolute value of the ratio must be greater than 1, or the proportion couldn't exceed $\frac{12}8$; but then the largest term dominates, so $$q^4 \approx \frac{819}{51} \approx 16.05$$ and th...
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about 1 month ago
Comment Post #284651 You can easily calculate the expected steps per roll as 1.68. To reach a million steps you're going to need at least 20000 rolls, and an estimated 595238 rolls. Is there anything which you can't calculate to sufficient precision for your purposes just using the central limit theorem?
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about 1 month ago
Comment Post #284550 `$\tilde{e}$` gives $\tilde{e}$
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about 2 months ago
Comment Post #284052 You seem to be amalgamating two orthogonal issues: citing the source of the material which the question is about, and establishing some kind of whitelist of acceptable sources. IMO the first is a reasonable issue to raise and the second is an unreasonable suggestion, but the discussion would be clear...
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3 months ago
Comment Post #283952 Yes, that's what I said in my comment yesterday.
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3 months ago
Edit Post #283111 Question closed 3 months ago
Comment Post #283935 @#53922 I think (although without more context I can't be certain) that you're misunderstanding the flow of the text. It looks to me as though (2.6) states a condition (which you've misquoted in your comment: that subscript $\alpha = 0$ is there for a reason) and then the following text, from "By the...
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3 months ago
Edit Post #283935 Initial revision 3 months ago
Answer A: Consider the second of these integrals (What's the meaning of second right here?)
> What did they mean by "second"? They've mentally expanded $$\frac{dJ}{d\alpha}=\int{x1}^{x2}\left(\frac{\partial f}{\partial y}\frac{\partial y}{\partial \alpha}+\frac{\partial f}{\partial \dot{y}}\frac{\partial \dot{y}}{\partial \alpha}\right)\mathrm dx$$ (which I've corrected to be what it say...
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3 months ago
Comment Post #282564 @#54204, I'm not sure what suggested edits you're talking about.
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3 months ago
Comment Post #283886 I don't think it's a duplicate as such, but you asked a [previous question](https://math.codidact.com/posts/282771) on a later sentence from this exact passage from your textbook (and Wolgwang kindly replaced your image with text and MathJax there, which you could reuse here).
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3 months ago
Comment Post #283899 @DNB, your teacher seems to have a vocabulary full of obscure English words which reference supernatural beings or supernatural knowledge of the future (*soothsay*, *augure*, *fey*, *sibylline*, *vaticinate*), but that vocabulary isn't suitable for use (a) in mathematics; (b) with native English spea...
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3 months ago
Edit Post #283713 Initial revision 4 months ago
Answer A: Find limits of integration in polar coordinates
You're going to need to differentiate the curves where they pass through the origin, and also find the angle of the intercept. $$\frac{\textrm{d}}{\textrm{d}x} \textrm{blue curve}\Big\vert{x=0} = 0$$ giving a limit $\theta0=0$. $$\frac{\textrm{d}}{\textrm{d}x} \textrm{red curve}\Big\vert{x=0} =...
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4 months ago
Comment Post #283400 Hint: you can find the answer near the start of the [Wikipedia page on matrices](https://en.wikipedia.org/wiki/Matrix_\(mathematics\)).
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4 months ago
Edit Post #283400 Post edited:
Escaping workaround
4 months ago
Edit Post #283518 Initial revision 4 months ago
Question Do these major triangle lines have names?
Kimberling's Encyclopedia of Triangle Centers lists, among other things, lines on which each centre is found, but usually listing only two points on the line. As a little project I've assembled these triples to find lines which have many centres, which would seem to be a rough measure of how importan...
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4 months ago
Comment Post #283399 @#53628, it's not an unreasonable assumption that someone with questions about material at this level is in full-time education and has access to a teacher.
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4 months ago
Edit Post #283433 Initial revision 4 months ago
Answer A: Finding the smallest Mersenne-number multiple of an odd integer
Add one to both sides and consider residues modulo $a$ to get $$2^n \equiv 1 \pmod a$$ So you want to find the multiplicative order of $2$ modulo $a$. As you note, $2^n \ge a + 1$ so $n \ge \lg(a+1)$; by Lagrange's theorem, $n \le \varphi(a)$, where $\varphi$ is Euler's totient function. More gene...
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4 months ago
Comment Post #283339 You do realise that this is the Mathematics site, not the Physics one?
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4 months ago
Comment Post #283299 Yes, and then we can see how well the "revert to previous version" feature is implemented.
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4 months ago
Edit Post #283301 Initial revision 4 months ago
Answer A: Is replacing the entire question with a different one appropriate?
No, this is not appropriate. If someone no longer wishes to keep their unanswered question on the site, they can delete it. If someone wishes to ask a new question, they can do so as a new question. The only reasons I can see for not behaving straightforwardly are (i) some idea that it's more ecol...
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4 months ago
Edit Post #283299 Initial revision 4 months ago
Answer A: Why was my question closed: If Alice must've have classes on at least 2 days, why do you need the intersection of 3 's?
1. It wasn't actually unilateral. 2. It's not so much that the question was unconstructive, as the wholesale replacement of the content which removed all context to the existing comment. The question was flagged as "seems like some weird attempt to game the system", which indeed it does. So I pos...
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4 months ago
Comment Post #283254 Does this really need two questions? There are marginal differerences to the other one, but really they're both asking for explanations of the same diagram, and if there's any answer other than "If that explanation doesn't help you, find a better one" then it's probably better in one place rather tha...
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4 months ago
Edit Post #282645 Question closed 4 months ago
Edit Post #283185 Initial revision 4 months ago
Answer A: Prove $(\cos^3\theta+\sin^3\theta)^2= \cos^6\theta(1+\tan^3\theta)^2$
$$(a+b)^2 = a^2 \left(1 + \frac ba\right)^2$$
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4 months ago
Comment Post #283161 @#53922, by $=$ I mean the "equals" symbol, which (I repeat) **does not appear** in the original text where you have placed it before the third line of the derivation. I'm 95% sure that the next part of the original text after the photograph included in the question will return to $$\lim_{h \to 0} {h...
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4 months ago
Comment Post #283161 I don't know which language the text around the notation is written in, but since the notation uses $=$ where appropriate I assume that it's significant that the line which uses $z$ instead of $a$ is preceded by text instead of $=$. Are you misreading the text and assuming a jump to a solution where ...
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4 months ago
Comment Post #282600 What makes you think that "*these authors and publishers are desperate for income*" as opposed to unsatisfied with the alternatives?
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4 months ago
Edit Post #283122 Initial revision 4 months ago
Answer A: Intuitively, why would organisms — that after one minute, will either die, split into two, or stay the same, with equal probability — all die ultimately?
This can be recast as a random walk on a line. Let $nt$ be the number of amoebae after $t$ events, and process the events in any order which makes sense. (It may help to think of this as serialising a parallel process on a single-core CPU). For example, you could choose to number the the amoebae by t...
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4 months ago
Edit Post #283121 Initial revision 4 months ago
Answer A: Why would skyrocketing the numbers of doors help laypeople intuit the Monty Hall Problem?
The only thing special about the door you chose is that you chose it, and you did so without any information, so objectively it isn't special at all. The door which the host leaves closed is special because it was chosen from the remaining doors by someone with information, so objectively it is actua...
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4 months ago
Edit Post #279044 Post edited:
A proposed edit tried to improve the typography with nbsp; this is a better fix
4 months ago
Comment Post #283086 Firstly, I don't see anything in the T&C on the physicsforums site which says that content is CC0-compatible, which is why I've deleted your self-answer. But secondly, even if it were, it's almost always better to write an answer in your own words once you've understood the solution to a more than su...
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4 months ago
Comment Post #282645 This question at present is completely different to the question originally posted and to which my previous comment applies. Recycling a question ID like that is a source of confusion. What's going on?
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4 months ago
Comment Post #283086 That sounds very broken. DuckDuckGo in an incognito browser window gives me a useful result from Wolfram MathWorld as the very first result.
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4 months ago
Comment Post #283086 What does your favourite search engine say?
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4 months ago
Comment Post #282658 @#8046 , go ahead.
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4 months ago
Comment Post #282658 I won't pretend to be enthusiastic about the idea, but I recognise that in small communities it's sometimes necessary to serve a term in office as a public duty. I have no prior experience as a moderator *per se*, but in another place I did have maximum rep-based privileges unlocked on one site and m...
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5 months ago
Comment Post #282642 If the quoted exercise is the true problem and this is an XY question, it's far simpler to consider the basic combinatorial meaning of $\binom{n}{k}$.
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5 months ago
Comment Post #282645 Probably not. But if you interpret $\sum_{k=0}^n k \binom{2n}{k}$ in terms of choosing a team of up to $n$ people with one designated captain from $2n$ people then you can transform it into a sum which you're already familiar with.
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5 months ago
Edit Post #282637 Initial revision 5 months ago
Answer A: A formal-logic formula for decimal to binary conversion
The formal formula for base conversion of a non-negative number is $$x = \left\lfloor \frac{x}{b} \right\rfloor b + (x \bmod b)$$ For binary, $b=2$.
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5 months ago
Comment Post #281319 @DNB, the sum total of your edits seems to be to remove all MathJax content. If you refer to explaining to a primary school pupil, I think the correct response is probably "The subject is too advanced. Wait a few years," but since I've never tried to teach maths to primary school pupils I may be unde...
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5 months ago
Edit Post #282564 Initial revision 5 months ago
Answer A: What story and TWO-digit Natural Numbers best fit Bayes' Theorem chart?
I flagged it as a duplicate. I don't recall seeing the subtle difference, and in any case it's your responsibility as the asker of both questions to put them in context with respect to each other: both of them link to an external site but don't mention the other question on this site. I still beli...
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5 months ago
Comment Post #282286 You ask whether questions "like these" are considered on-topic, but give the example in a format which only moderators can actually read (a link to a deleted question). That doesn't seem very productive. (Although, FWIW, my attempt to reconstruct the question from clues in this meta-question suggests...
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5 months ago
Comment Post #281724 Would I be correct in guessing that the lack of any comment on my answer is because you haven't seen the final version?
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6 months ago
Comment Post #281987 This appears to be exactly the same as your earlier question https://math.codidact.com/posts/280741 , and certainly suffers the same flaw that I raised then in the comments which makes it unanswerable.
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6 months ago
Edit Post #281764 Post edited:
Complete argument
7 months ago
Edit Post #281764 Post edited:
Actually I was a bit too blithe in how easy it is to show congruence
7 months ago
Edit Post #281764 Post edited:
7 months ago
Edit Post #281764 Initial revision 7 months ago
Answer A: proving relative lengths on a secant
This image matches the description in the question (note that, in violation of what I consider to be conventional, $O$ is not the centre of the circle but the midpoint of $AD$). I add a perpendicular to $AD$ from $O$ which intersects $AC$ at $G$, and lines $OF$ and $DG$ which intersect at $H$. As ...
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7 months ago
Edit Post #281319 Initial revision 8 months ago
Answer A: How can I deduce which operation removes redundacies?
> 1. How can I deduce which operation ought fill in the red blank beneath? You can't. It's a hideous phrasing. The issue at question is not "redundancies" (which would carry the implication that they're merely unnecessary) but multiple counting: that is, counting the same assignment more than onc...
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8 months ago
Comment Post #280851 Do you have a definition of $\lim_{a \to \infty} f(a) = \infty$ in first order logic (i.e. as a simple statement with $\exists$ and $\forall$)?
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10 months ago
Comment Post #280741 How are you quantifying "contrast the base rate fallacy"?
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10 months ago
Comment Post #280639 @TechnologicallyIlliterate, yes. The wording around arbitrary constants and families of solutions indicates that you need to be more careful than just eliminating the common $y$. The $c$ is (32) is not necessarily equal to the $c$ in (33).
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10 months ago
Edit Post #280639 Post edited:
10 months ago
Edit Post #280639 Initial revision 10 months ago
Answer A: Isn't it wrong to write that Indefinite Integral = Definite Integral with a variable in its Upper Limit?
> ${\int{f(t) \\; dt} = \int{t0}^t f(s) \\; ds \quad \text{ where $t0$ is some convenient lower limit of integration.}}$ isn't actually in the source text at all. Unpacking some of the surrounding text to more formal notation, it goes from equation (32) $$\exists c: \mu(t) y = \int \mu(t) g(t) \\...
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10 months ago
Comment Post #278332 For $n=3$ you want three rectangles of 1/3 by 1. Beyond there it gets more complicated; I suspect that the initial cuts will tend to leave a rough circle, but if so then IIRC some calculations I made a few months ago showed that the diameter of a sector sliced from the circle would eventually be grea...
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11 months ago
Comment Post #280068 @Derek Elkins, I would say that the key difference is that division by 2 isn't really division in binary floating point representations: it's subtraction applied to the exponent. (I'm sure you know this already, but I didn't think it came through clearly in the explanation).
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12 months ago
Comment Post #280118 To be clear: am I correct to understand that by "*the last two points*" you mean everything from "*and we define*" until the end?
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12 months ago
Comment Post #279400 What is the division ring in your "intuitive" instantiation?
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about 1 year ago
Comment Post #278431 Or the property $P(x) = x \not\in x$ cannot exist in such an axiomatic system, or such an axiomatic system can contain a set of all sets but at the cost of consistency, or possibly such an axiomatic system can contain a set of all sets as long as it doesn't have the law of the excluded middle.
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about 1 year ago
Comment Post #278270 Note to site admins: I haven't wrapped the multiline stuff in `$$` because it was rendering identically in the preview. IMO it would be a perfectly reasonable approach to look for/write a Markdown plugin to treat the MathJax delimiters `$` and `$$` as start and end delimiters of a section where escap...
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about 1 year ago
Comment Post #278270 @Derek, now that you mention it, I'd noticed that I had to escape the backslashes for backslash-curlybrace to get the multiset notation to work. I should have put 2 and 2 together myself. Thanks for the diagnosis.
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about 1 year ago
Comment Post #278269 @tommi, see https://math.codidact.com/q/278270
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about 1 year ago
Edit Post #278270 Initial revision about 1 year ago
Question MathJax config: newlines in eqnarray contexts
In my answer to https://math.codidact.com/questions/278268 I have a couple of `eqnarray` contexts which are being rendered by MathJax but aren't being broken into lines as they should. This works fine in other sites with MathJax which I used to use, so I suspect that it's a problem with the configura...
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about 1 year ago
Edit Post #278269 Initial revision about 1 year ago
Answer A: Asymptotics of counting integers by prime signature
Let $\alpha$ be the smallest exponent such that we know how to calculate $\pi(n)$ in time $\tilde O(n^\alpha)$. Courtesy of Deléglise and Rivat, who removed the $+ \epsilon$ from Lagarias, Miller and Odlyzko's bound, we know that $\alpha \le \tfrac23$, but I'm going to work in terms of $\alpha$ becau...
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about 1 year ago
Edit Post #278268 Initial revision about 1 year ago
Question Asymptotics of counting integers by prime signature
The prime counting function $\pi(n)$ which counts the number of primes up to $n$ is well-known, and it's also fairly well-known that using a well-optimised implementation of the Meissel-Lehmer algorithm it can be calculated in $\tilde O(n^{2/3})$ time. What about numbers of other forms? To be spec...
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about 1 year ago
Comment Post #278141 The case $k=1$ is also easy: we take $X = \max_{i=1}^n(X_i)$ and observe that for $x \in [1, s]$, $P(X \le x) = \left(\frac{x}{s}\right)^n$ because each independent die must roll no more than $x$. From that we can get $P(X = x)$ in closed form and $E(X)$ in terms of Faulhaber's formulas.
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about 1 year ago