Activity for Peter Taylorâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #282637 | Initial revision | — | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #282564 | Initial revision | — | over 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) |
— | over 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) |
— | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #281764 |
Post edited: Complete argument |
— | over 3 years ago |
| Edit | Post #281764 |
Post edited: Actually I was a bit too blithe in how easy it is to show congruence |
— | over 3 years ago |
| Edit | Post #281764 |
Post edited: |
— | over 3 years ago |
| Edit | Post #281764 | Initial revision | — | over 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) |
— | over 3 years ago |
| Edit | Post #281319 | Initial revision | — | over 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) |
— | over 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) |
— | almost 4 years ago |
| Comment | Post #280741 |
How are you quantifying "contrast the base rate fallacy"? (more) |
— | almost 4 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) |
— | almost 4 years ago |
| Edit | Post #280639 |
Post edited: |
— | almost 4 years ago |
| Edit | Post #280639 | Initial revision | — | almost 4 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) $$\exists c: \mu(t) y = \int \mu(t) g(t) \\... (more) |
— | almost 4 years ago |
| Comment | Post #278332 |
For $n=3$ you want three rectangles of 1/3 by 1. Beyond there it gets more complicated; I suspect that the initial cuts will tend to leave a rough circle, but if so then IIRC some calculations I made a few months ago showed that the diameter of a sector sliced from the circle would eventually be grea... (more) |
— | almost 4 years ago |
| Comment | Post #280068 |
@Derek Elkins, I would say that the key difference is that division by 2 isn't really division in binary floating point representations: it's subtraction applied to the exponent. (I'm sure you know this already, but I didn't think it came through clearly in the explanation). (more) |
— | almost 4 years ago |
| Comment | Post #280118 |
To be clear: am I correct to understand that by "*the last two points*" you mean everything from "*and we define*" until the end? (more) |
— | almost 4 years ago |
| Comment | Post #279400 |
What is the division ring in your "intuitive" instantiation? (more) |
— | about 4 years ago |
| Comment | Post #278431 |
Or the property $P(x) = x \not\in x$ cannot exist in such an axiomatic system, or such an axiomatic system can contain a set of all sets but at the cost of consistency, or possibly such an axiomatic system can contain a set of all sets as long as it doesn't have the law of the excluded middle. (more) |
— | about 4 years ago |
| Comment | Post #278270 |
Note to site admins: I haven't wrapped the multiline stuff in `$$` 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) |
— | about 4 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) |
— | about 4 years ago |
| Comment | Post #278269 |
@tommi, see https://math.codidact.com/q/278270 (more) |
— | about 4 years ago |
| Edit | Post #278270 | Initial revision | — | about 4 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) |
— | about 4 years ago |
| Edit | Post #278269 | Initial revision | — | about 4 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) |
— | about 4 years ago |
| Edit | Post #278268 | Initial revision | — | about 4 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) |
— | about 4 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) |
— | about 4 years ago |