Activity for Peter Taylor
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #296596 |
The transcript contains more noise than pertinent information, but what it completely missing is any description of the game (I assume) which is being played, and that's by far the most important thing to understand what's going on mathematically. (more) |
— | 21 days ago |
| Edit | Post #296596 | Question closed | — | 21 days ago |
| Edit | Post #296599 | Question closed | — | 21 days ago |
| Comment | Post #296599 |
One plausible explanation is that Vadim Ponomarenko's point is about expected value being a sum/integral over events of the value of the event weighted by the probability of the event, but if you want to know what they mean you should try asking them rather than random people on the Internet. (more) |
— | 21 days ago |
| Edit | Post #296534 | Initial revision | — | about 1 month ago |
| Answer | — |
A: please showcase two posts from Kenneth Rosen's Discrete Mathematics? Those posts were about comprehension of the English language, not about mathematics. If you have a question about the mathematical content of the book then you can create a new post. (more) |
— | about 1 month ago |
| Comment | Post #296272 |
There is also the less ambiguous $83 \equiv 98 \pmod 5$, which it seems to me TeX pushes people towards using by having weird spacing on `\mod`. This may be because TeX was written by someone who straddles maths and compsci.
With respect to Latin, I think it's probably dative ("to the modulus"... (more) |
— | 3 months ago |
| Comment | Post #296180 |
This needs more context to be intelligible. Where did Newton use quantifiers in his method of fluxions? What are $x-$ and $h-$terms? (more) |
— | 4 months ago |
| Comment | Post #296101 |
@#118341, it's the notation that I don't understand, although I think maybe I've figured it out. Is $\Delta_s^k$ supposed to denote the $k$th difference operator with respect to $s$? If so, I think it would be a lot clearer to write the initial function as $f_{even}(x)=\sum_{k=0}^\infty G(k)\frac... (more) |
— | 4 months ago |
| Comment | Post #296101 |
What's the point of $G^*$? I don't see how it accomplishes
> interpolation of consecutive derivatives over even points so to get the values at odd points
because there's no indication of how to derive $\Delta_s^k$ for half-integer $s$ from the values for integer $s$. (more) |
— | 4 months ago |
| Comment | Post #296061 |
What does "infinite 2-d volume both above and below $y = 0$" mean? Is it that $\int |\mathcal{G}(x)| \pm \mathcal{G}(x) \textrm{d}x = \infty$ for both choices of sign? If so, it's not at all clear to me how the example meets this criterion. (more) |
— | 5 months ago |
| Comment | Post #295469 |
@#116526, if you don't understand your own question well enough to write a title for it or to make your own critique of proposed titles, you're probably asking questions at the wrong level. I would suggest that rather than trying to crowdsource an answer to an ill-defined question by pitting peop... (more) |
— | 5 months ago |
| Comment | Post #295983 |
In addition to providing preliminaries, I don't think this is even complete. How does $\mathcal S$ determine $p$, for example? (more) |
— | 5 months ago |
| Edit | Post #295914 | Initial revision | — | 5 months ago |
| Answer | — |
A: Guidelines for writing question bodies when one is self-answering I would not advise inventing a ficticious confusion: that only serves to confuse the reader. Explaining why the theorem is interesting is definitely worthwhile. I would add that the conjunction of Q&A should add value. Standard theorems with standard proofs would be clutter. When I have create... (more) |
— | 5 months ago |
| Comment | Post #295864 |
I think the footnote 1 is supposed to say that $\frac12 n(n+1) = \frac12( (n+\frac12)^2 - \frac14)$. Perhaps it's even simpler to say that $n(n+1) = (-n-1)(-n)$ and so that except for $n = \frac{p-1}2$ they pair up. (more) |
— | 5 months ago |
| Edit | Post #295846 | Initial revision | — | 6 months ago |
| Answer | — |
A: Consequences of NP-Complete in QP? > With NPI being NP-Intermediate, problems which require quasi-polynomial complexity to solve. No, NPI is problems in NP which are not in P and are not in NPC. The only claims about complexity which follow easily from the definition are that they take superpolynomial but no worse than exponent... (more) |
— | 6 months ago |
| Edit | Post #295560 | Initial revision | — | 7 months ago |
| Answer | — |
A: Increasing the chances of getting a research question answered? As a prefatory remark, I should make clear that I don't understand the mathematics in your question. However, one problem which has already been mentioned is that readers who understand measure theory are nevertheless unable to understand the terminology of the question. The same applies to th... (more) |
— | 7 months ago |
| Edit | Post #295558 | Initial revision | — | 7 months ago |
| Answer | — |
A: Why are regular languages closed under intersection and complementation? > Recall that a regular language is a language accepted by a nondeterministic finite automaton (NFA) This is true, and for some purposes it's the most useful perspective, but there's an alternative perspective which is more useful for proving this type of property. A regular language is a lang... (more) |
— | 7 months ago |
| Comment | Post #285086 |
I think the unofficial PE Discord is probably a more appropriate place to advertise than the forum. (more) |
— | 7 months ago |
| Comment | Post #294222 |
I'm no topologist, but on the first surface I can draw a closed path and select two points such that any path between them must intersect the first path. I'm pretty sure that's not possible on the second. (more) |
— | about 1 year ago |
| Edit | Post #292896 | Initial revision | — | almost 2 years ago |
| Answer | — |
A: Should there be more than one sort of math community? It's not always easy to draw the line. I read this question just now because it was bumped, and immediately thought of this question. It was, at least in part, a question about philosophy of mathematics, but I don't think the asker realised that. Their goal was to understand the context of a pape... (more) |
— | almost 2 years ago |
| Comment | Post #292671 |
Two independent points: 1. "Convex hull" suggests an underlying set which you're bounding. The description of your data would fit better with the term "convex polytope", which may help you search the literature. 2. "the edge... normal to the vector $\vec{G}_j$" suggests that you're working in 2D.... (more) |
— | almost 2 years ago |
| Edit | Post #292629 | Question closed | — | almost 2 years ago |
| Comment | Post #292629 |
It's not reasonable to expect people on this website to define terms which appear to have been invented by someone on another website when we can't even read the original post without creating an account. In addition, the real question here appears to be non-mathematical: how can I tell my boss t... (more) |
— | almost 2 years ago |
| Comment | Post #292332 |
I think there may be an interesting question in here somewhere, but it needs some work to bring it out. My first impression when reading it was that it is rather confusing. Who are Barsky and Benzaghou, and why is it relevant that they in particular haven't proved something that no-one has proved... (more) |
— | about 2 years ago |
| Edit | Post #292317 |
Post edited: A few small translations from Spanish |
— | about 2 years ago |
| Comment | Post #292268 |
Doesn't the hint also require the unstated assumption that $0 \in \Omega$? (more) |
— | about 2 years ago |
| Comment | Post #292178 |
I checked the top-left of the table, reading antidiagonals in both directions, and found nothing in OEIS. This is mildly surprising, but it rules out some obvious guesses. (more) |
— | about 2 years ago |
| Comment | Post #292112 |
On the positive side, it's sufficient to show that $f(p) = p$ for all primes $p$. If so then for each $1 \le a < p$ there is a prime $q = a + mp$ by Dirichlet's theorem on arithmetic progressions: then $f(q) \equiv a \pmod p$ and since each equivalence class maps to a single equivalence class thi... (more) |
— | about 2 years ago |
| Comment | Post #292112 |
It gets messy trying to push it. $f(5) \equiv 5 \pmod {12}$ follows from previous observations; $f(5) \in \\{0, 4\\} \pmod 5$ follows because the other equivalence classes are already accounted for. Then $f(5) - 1$ must be a power of two (it must be $5$-smooth and coprime to $3$ and $5$); $f(5) -... (more) |
— | about 2 years ago |
| Comment | Post #292112 |
Then the original property is equivalent to the pair of properties: $\forall p \textrm{ prime}: f(a) \equiv f(b) \pmod p \iff a \equiv b \pmod p$ and $\forall p \textrm{ prime}: f(p) \equiv 1 \pmod {p-1}$. By Dirichlet's theorem on arithmetic progressions we have that for every prime $p$ there ar... (more) |
— | about 2 years ago |
| Comment | Post #292112 |
Actually we can argue that for each prime $p$ there is a $c_p$ such that $f(p) = c_p(p-1) + 1$. If $f(n) \bmod p$ takes fewer than $p$ distinct values then by the pigeonhole principle there must be $a \not\equiv b$ for which $f(a) \equiv f(b)$ and we can derive a contradiction from $f(a)^{f(p)} \... (more) |
— | about 2 years ago |
| Comment | Post #292112 |
$f(a)^{f(p)}\equiv f(a)\pmod p$ is satisfied if (but not only if) $f(p) \equiv 1 \pmod{p-1}$, i.e. $f(p) = c_p (p-1) + 1$. But there's no reason *a priori* why $c_p$ should be the same for all primes, or why $f(n)$ should be $c(n-1) + 1$ for non-prime $n$. I think you've only considered a negligi... (more) |
— | about 2 years ago |
| Comment | Post #292113 |
What I see in the browser console is a 404 for amsmath.js. Does the post actually rely on amsmath? Maybe removing that `require` is the solution. (more) |
— | about 2 years ago |
| Edit | Post #292062 |
Post edited: Fix typos |
— | about 2 years ago |
| Comment | Post #291916 |
When $n=1$ the two options for $h$ are $g_-$ and $g_+$, whose domains intersect only at $[\frac12,\frac12]$. If all of the domains at level $n$ intersect only at irrelevant points then at $n+1$ each $h_n$ becomes $h_n(g_-(x))$ and $h_n(g_+(x))$, which splits the domain of $h_n$ into two parts whi... (more) |
— | about 2 years ago |
| Edit | Post #291919 | Initial revision | — | about 2 years ago |
| Answer | — |
A: How can we prove that a point that follows another point has the same trajectory given a contant angle and ratio? The dot product cannot be sufficient because even making substitutions to minimise the occurrences of $Q$ we get $$\cos(\alpha)=\frac{\overrightarrow{P(t)}\cdot\overrightarrow{Q(t)}}{k|\overrightarrow{P(t)}|^2}$$ there are two solutions in the plane. I personally would tackle this by complex n... (more) |
— | about 2 years ago |
| Edit | Post #291916 | Initial revision | — | about 2 years ago |
| Answer | — |
A: Formalizing proof of existence of roots of functional equation All real roots are in $[0, 1)$. If $x \le 0$ then $f(x) \le x$ with equality only at $x = 0$. By induction, for all $n \in \mathbb{N}$ and $x \le 0$ we have $f^n(x) \le x$ with equality only at $x = 0$. If $x \ge 1$ then $f(x) \le 0$, so for all $n \in \mathbb{N}$ we have $f^n(x) \le 0 &dag... (more) |
— | about 2 years ago |
| Comment | Post #291911 |
$f^n(x) - x$ is a polynomial of degree $2^n$, so it has $2^n$ roots. Is your goal essentially to prove that those roots are distinct real numbers in the interval $[0, 1)$? (more) |
— | about 2 years ago |
| Comment | Post #290765 |
@#8046, yes, I did. (more) |
— | about 2 years ago |
| Comment | Post #291827 |
It's not necessary to ask the same question three times, much less on the same day. (more) |
— | about 2 years ago |
| Edit | Post #291828 | Question closed | — | about 2 years ago |
| Comment | Post #290765 |
@#80779, physics has nothing to do with this discussion, but the question and the answer are both about philosophy of mathematics, so if your comments aren't philosophical then they're definitely missing the point. *Multiverse* here is a term taken from the paper which the question asks about. (more) |
— | over 2 years ago |