Activity for Peter Taylor
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #282600 |
What makes you think that "*these authors and publishers are desperate for income*" as opposed to unsatisfied with the alternatives? (more) |
— | over 2 years ago |
| Edit | Post #283122 | Initial revision | — | over 2 years 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... (more) |
— | over 2 years ago |
| Edit | Post #283121 | Initial revision | — | over 2 years 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... (more) |
— | over 2 years ago |
| Edit | Post #279044 |
Post edited: A proposed edit tried to improve the typography with nbsp; this is a better fix |
— | over 2 years 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... (more) |
— | over 2 years 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? (more) |
— | over 2 years 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. (more) |
— | over 2 years ago |
| Comment | Post #283086 |
What does your favourite search engine say? (more) |
— | over 2 years ago |
| Comment | Post #282658 |
@#8046 , go ahead. (more) |
— | almost 3 years 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... (more) |
— | almost 3 years 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 $\binom{n}{k}$. (more) |
— | almost 3 years 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. (more) |
— | almost 3 years ago |
| Edit | Post #282637 | Initial revision | — | almost 3 years 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, $b=2$. (more) |
— | almost 3 years 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... (more) |
— | almost 3 years ago |
| Edit | Post #282564 | Initial revision | — | almost 3 years 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... (more) |
— | almost 3 years 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... (more) |
— | almost 3 years 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? (more) |
— | almost 3 years 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. (more) |
— | almost 3 years ago |
| Edit | Post #281764 |
Post edited: Complete argument |
— | almost 3 years ago |
| Edit | Post #281764 |
Post edited: Actually I was a bit too blithe in how easy it is to show congruence |
— | almost 3 years ago |
| Edit | Post #281764 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #281764 | Initial revision | — | almost 3 years 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 ... (more) |
— | almost 3 years ago |
| Edit | Post #281319 | Initial revision | — | about 3 years 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... (more) |
— | about 3 years 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 $\forall$)? (more) |
— | about 3 years ago |
| Comment | Post #280741 |
How are you quantifying "contrast the base rate fallacy"? (more) |
— | about 3 years 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). (more) |
— | about 3 years ago |
| Edit | Post #280639 |
Post edited: |
— | over 3 years ago |
| Edit | Post #280639 | Initial revision | — | over 3 years 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) $$\exists c: \mu(t) y = \int \mu(t) g(t) \\... (more) |
— | over 3 years ago |
| Comment | Post #278332 |
For $n=3$ you want three rectangles of 1/3 by 1. Beyond there it gets more complicated; I suspect that the initial cuts will tend to leave a rough circle, but if so then IIRC some calculations I made a few months ago showed that the diameter of a sector sliced from the circle would eventually be grea... (more) |
— | over 3 years ago |
| Comment | Post #280068 |
@Derek Elkins, I would say that the key difference is that division by 2 isn't really division in binary floating point representations: it's subtraction applied to the exponent. (I'm sure you know this already, but I didn't think it came through clearly in the explanation). (more) |
— | over 3 years ago |
| Comment | Post #280118 |
To be clear: am I correct to understand that by "*the last two points*" you mean everything from "*and we define*" until the end? (more) |
— | over 3 years ago |
| Comment | Post #279400 |
What is the division ring in your "intuitive" instantiation? (more) |
— | over 3 years ago |
| Comment | Post #278431 |
Or the property $P(x) = x \not\in x$ cannot exist in such an axiomatic system, or such an axiomatic system can contain a set of all sets but at the cost of consistency, or possibly such an axiomatic system can contain a set of all sets as long as it doesn't have the law of the excluded middle. (more) |
— | over 3 years ago |
| Comment | Post #278270 |
Note to site admins: I haven't wrapped the multiline stuff in `$$` 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... (more) |
— | over 3 years 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. (more) |
— | over 3 years ago |
| Comment | Post #278269 |
@tommi, see https://math.codidact.com/q/278270 (more) |
— | over 3 years ago |
| Edit | Post #278270 | Initial revision | — | over 3 years 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... (more) |
— | over 3 years ago |
| Edit | Post #278269 | Initial revision | — | over 3 years 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... (more) |
— | over 3 years ago |
| Edit | Post #278268 | Initial revision | — | over 3 years 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... (more) |
— | over 3 years 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. (more) |
— | over 3 years ago |
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