Activity for r~~
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #286832 | Initial revision | — | almost 2 years ago |
| Answer | — |
A: Show that $f(x) = \arctan\left(\frac{x}{x+1}\right) + \arctan\left(\frac{x+1}{x}\right) = \frac{\pi}{2}$ You're right that division by zero is a problem if you want to use that identity. Rather than salvage that, I would recommend this identity instead: $$ \arctan a + \arctan{a^{-1}} = \frac\pi2\qquad\text{for positive $a$} $$ Proving this identity is easy: draw a $1 \times a$ rectangle with a d... (more) |
— | almost 2 years ago |
| Edit | Post #286167 |
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— | about 2 years ago |
| Edit | Post #286167 | Initial revision | — | about 2 years ago |
| Answer | — |
A: Complex numbers in 2D, quaternions in 4D, why nothing in 3D? Intuition is a personal thing, but here are some thoughts that might be useful. (Rigorous justifications for most claims are absent, to keep this post from getting too long. I intend to restrict myself merely to pointing suggestively and waggling my eyebrows.) Don't think of the quaternion trick a... (more) |
— | about 2 years ago |
| Comment | Post #286130 |
Have you tried it to see what happens? (more) |
— | about 2 years ago |
| Comment | Post #285819 |
Doesn't $\varphi$ convex (and defined) everywhere imply that $\varphi$ is continuous, by a very standard result? (more) |
— | about 2 years ago |
| Edit | Post #285681 |
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— | over 2 years ago |
| Comment | Post #285681 |
I'll edit my answer to include that information if you edit your question to incorporate my feedback (remove the irrelevant content related to Rothe-Hagen, including the incorrect assertion that Rothe-Hagen is a generalization of GVI) and include this more specific request.
I feel like I harp on t... (more) |
— | over 2 years ago |
| Edit | Post #285681 |
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— | over 2 years ago |
| Edit | Post #285681 | Initial revision | — | over 2 years ago |
| Answer | — |
A: How can a 15 year old construe the LHS of Generalized Vandermonde's Identity, when it lacks summation limits and a summation index? Unfortunately, this is ambiguous notation. It isn't your fault; this presentation of this identity is more suited for an audience already familiar with the material than someone learning it for the first time. The answer to your question is that the summation is over all ordered length-$p$ sequenc... (more) |
— | over 2 years ago |
| Comment | Post #285680 |
This is just a question about Vandermonde, not Rothe-Hagen; I suggest removing the Rothe-Hagen content.
(It's not the case that either of the two identities quoted are generalizations of each other; both are different ways to generalize the original Vandermonde identity. But this is a total aside ... (more) |
— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #285072 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What is the parallel for edges? I would still use the term ‘edge’ for that case—as in, ‘These three arcs are the edges of a circular triangle.’ If necessary to prevent confusion, I might specify ‘curved edge’ or something similar. But while ‘edge’ in geometry often implies a strict line segment, in graph theory it simply denotes a ... (more) |
— | over 2 years ago |
| Comment | Post #285015 |
^ This. Honestly, actually following this advice on all of your intuition questions would improve most of them substantially.
But note that these are not examples of following this advice: ‘I don't understand.’ ‘How can this be?’ ‘This is sortilege!’
Instead:
* Connect the thing you're askin... (more) |
— | over 2 years ago |
| Comment | Post #284997 |
All the above is true even in the absurdly unlikely case (perhaps you don't realize just how idiosyncratic your writing style is) that you've reposted someone else's closed question verbatim. You still know it's a question that doesn't meet SE's standards, and so you've decided to try it out here ins... (more) |
— | over 2 years ago |
| Comment | Post #284997 |
I don't think you understand. This question isn't closed because it's a repost from SE. This question is closed because it's a bad question. It would be a bad question regardless of whether it was original or a repost. However, the fact that it's a repost of a closed question means that not only have... (more) |
— | over 2 years ago |
| Comment | Post #284996 |
I recommend editing your question to be that, if that's what it is. The thing about a minimal border around two points is still imprecise; if that's an important part of the question, explain a bit more, and otherwise remove it. (more) |
— | over 2 years ago |
| Comment | Post #284997 |
of calling for a proof-by-picture by linking to a question the premise of which is that proofs-by-picture are often misleading and that students should pay more attention to stuff like algebra. Hopefully this is you poking a little fun at yourself, and not... a less charitable interpretation. (more) |
— | over 2 years ago |
| Comment | Post #284997 |
This was closed Somewhere Else (https://math.stackexchange.com/questions/4314855/without-trial-and-error-averageaveragea-b-c-vs-averagea-averageb-c), and should be closed here for the same reason. You got good feedback on that post, ignored it, and submitted exactly the same question here without try... (more) |
— | over 2 years ago |
| Comment | Post #284996 |
I believe there's a lovely question in here somewhere but it hasn't emerged yet. Some questions for you: What do you mean by ‘dot’? Do you mean the same thing as ‘point’, or are you using a different word intentionally to signify something else? Is a ‘minimal border around ... two dots’ something oth... (more) |
— | over 2 years ago |
| Edit | Post #284909 |
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— | over 2 years ago |
| Edit | Post #284909 |
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— | over 2 years ago |
| Edit | Post #284907 |
Post edited: Retagging |
— | over 2 years ago |
| Suggested Edit | Post #284907 |
Suggested edit: Retagging (more) |
helpful | over 2 years ago |
| Edit | Post #284909 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Third kind of infinite By Cantor's diagonal argument, there can be no bijection between the power set of any set and the set itself. This is true for finite and infinite sets. So taking the power set ($\mathcal P$) of a set of some infinite cardinality always gives you a set with a strictly larger infinite cardinality. ... (more) |
— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #284742 |
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— | over 2 years ago |
| Edit | Post #284742 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What does upper indices represent? A textbook homework problem might ask, ‘Speedy the snail creeps along at a steady pace of 60 cm per minute. How far does Speedy travel each second?’ The correct answer is, of course, one centimeter. Hopefully your teacher would also accept 10 mm or 0.01 m as equally valid answers; after all, they all... (more) |
— | over 2 years ago |
| Edit | Post #284741 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Can the bijection for the Lost Boarding Pass Probability Problem, be formulated or pictured? The bijection is just to swap the people sitting in the first and last seats. I feel like a ‘formula’ is more machinery than this simple concept is worth, but here, if this helps: let $P$ be the set of permutations on $\\{0\ldots n - 1\\}$, where for $p \in P$, $p(s)$ is the number of the passenge... (more) |
— | over 2 years ago |
| Comment | Post #284723 |
Any expression that yields the result of addition seems like it would be pretty much just addition. But, for example, perhaps you'd be happy with something like $\ln{e^a e^b}$? If not, maybe you could be clearer about what you would and would not accept. (more) |
— | over 2 years ago |
| Edit | Post #284557 |
Post edited: Typo |
— | over 2 years ago |
| Comment | Post #284561 |
Your source might be using [Einstein notation](https://en.wikipedia.org/wiki/Einstein_summation), but there are other notations that give different meanings to upper and lower indices. I think you need to include more of the surrounding context to know for sure—a raised index doesn't universally mean... (more) |
— | over 2 years ago |
| Suggested Edit | Post #284557 |
Suggested edit: Typo (more) |
helpful | over 2 years ago |
| Comment | Post #284551 |
Cheers, I added a paragraph that should clear that up. (more) |
— | over 2 years ago |
| Edit | Post #284551 |
Post edited: Clarify ‘abstract vector’ and tighten up some math expressions |
— | over 2 years ago |
| Edit | Post #284551 |
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— | over 2 years ago |
| Edit | Post #284551 | Initial revision | — | over 2 years ago |
| Answer | — |
A: transpose matrix and general matrix is completely messed up I suspect what's tripping you up here is the difference between applying a linear transformation to a vector versus applying a change of basis. Both involve matrix multiplication, but the nature of the transformation is different. First, some words about vectors. There are two ways to introduce st... (more) |
— | over 2 years ago |
| Edit | Post #284284 |
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— | over 2 years ago |
| Suggested Edit | Post #284284 |
Suggested edit: (more) |
helpful | over 2 years ago |
| Edit | Post #284281 |
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— | over 2 years ago |