darklight03/StackMIAsub huggingface dataset:
i have problem to determine if the word bake is transitive or intransitive verb from the Phrase "Samantha can bake at any time of the day." i am reading from a book called English grammar understanding the basic it say Action verbs that act upon something are called transitive verbs. Action verbs that do not act upon something are called intransitive verbs. If a verb (in any of its forms) can be put in one of the following slots, it is transitive: (a) What did you_____? (b) Who did you______ ? If a verb cannot be put in one of these slots, it is intransitive. If a verb (in one of its forms) can be put in one of the following slots, it is transitive: (a) He _____ something. (b) He____ someone. If a verb (in one of its forms) can be put in the following slot, it is intransitive: He____ by following the grammar i can say "he bake something" or "what did you bake" it look transitive for me
Since we have working models for forces "combining" or being describable via a single framework at higher energies (such as the "electroweak" force and the aim of GUTs), does electromagnetism split into an "electric" force and a "magnetic" force at lower energies, or is this simply a misnomer in the English language born of the order in which the behaviors where discovered and related? As an aside, the main reason I ask is because I have heard "spin" (the quantum number; which I might add in hindsight was badly named if considering the laymen such as myself) described as a "magnetic moment", and something entirely disconnected from "electric charge" (another quantum number); to my limited knowledge, there is no known meaningful correlation between the two properties (though obviously I might have just not read about/understood such). I'm a confused layman, and any answers will be much appreciated!
Looking around trying to find questions concerning the intuition behind discrete/indiscrete topologies, I haven't found much towards the essence of what these particular topologies imply about the space (and why it is meaningful). I realize that in a discrete topology, every set is both closed and open, as is the case with the indiscrete topology, however that the topologies are disconnected and connected respectively. That this somehow tells us about distinguishability between points; in the case of the discrete topology we have that every set of points can be at least disconnected from other sets of points, and that in the indiscrete topology, this is not the case. Now the difference between the neighborhoods then would be then that for the Indiscrete topology, all the neighborhoods include all other points, but that in the discrete topology each point has a neighborhood which doesn't include the other points. Am I correct so far? But I know there is much more, could someone expound on the intuition what is going on, maybe even including things such as levels of "seperated-ness", and perhaps what happens in between the Indiscrete and Discrete Topologies? Thanks, Brian
If I fill a plastic ziploc-shaped bag with water, the cross section profile should be sort of teardrop shaped (assuming we ignore the edge effects of the bag being sealed on the sides as well as the top and bottom). The bag should "sag"/get wider until to get the center of gravity as low as possible. Initially, getting wider will let more water towards the bottom but eventually this is offset by the bottom of the bag moving up (because the sides are fixed length). Is there a common function that describes the shape the cross-section of the bag makes? I would guess the bottom is a parabola, since gravity likes to make parabolas. Then I would guess the top is linear because its under tension. But I have no idea what the transition region might look like and whether you could put those two together into a nice function.
Are the slang usages of "bud" (mainly meaning cannabis, and occasionally clitoris, from what I understood) prevalent enough that I should avoid using them in a product intended for international availability? Example sentences which could be printed: "John has created a bud here!" "Share this bud!" (ouch) "Create bud" I would appreciate very much if you could state which part of the world you're from when answering this question. Some context: The lexical field surrounding a service I'm designing revolves around trees, plants, and nature in general. My team and I are in the process of selecting names for the various parts of the service, and we are struggling with one: It should depict something with potential, which is not yet fully developed, but holds the bases for future interactions. Seed would not be relevant, as this part of the service is sprouting from something we called a Tree, and I feel it would generate confusion about which one generates the other. Bud came to mind, and seems a good choice. it fits wery well with the rest of our service part's names. However, it does not seem to be a very commonly used word (much less than "tree", "branches", "leaves", "roots" and so on), and I'm afraid this could heighten the chances of it to be read in an alternate meaning. This item could be named a Leaf as well, which conveys a less accurate meaning, but possibly avoids this problem.
Is there a logical story behind this phrase? Because when looked at from a naive perspective, giving somebody their own medicine sounds like a kind thing to do as it would only treat their illness. The phrase only makes sense in the context of someone who knowingly sells poison as medicine, which is a rather rare thing (or was it common in the old times?). The most popular origin story I could find about "dose/taste of one's own medicine" is a tale where a cheat sells a medicine that does nothing, then gets sick and people give him his own medicine. And even with this background, it makes little sense, as the medicine doesn't sound like it harms him. Does anybody know the name of this story? Perhaps there's more depth to it.
The smallest possible cardinality of a base is called the weight of the topological space. I was wondering if all minimal bases have the same cardinality, and if every base contains a subset whose cardinality is the weight of the topological space? What aspects are common between a (smallest) base of a topology and a base of a vector space, besides the following similarity (open subset <-> vector, union <-> linear combination): every open subset is the union of some members in the base; every vector is the linear combination of some members in the base. Note that a base in a vector space is also a base in the linear matroid. Not sure if we can have some nice structure like matroid for a topological space to understand its (smallest) bases. Thanks and regards!
My daughter said to me this morning (the context is irrelevant): Er, it's all wet! The interjection I have written here as Er was synonymous with Yuck. Its wetness did not cause great happiness. But what's the right way to write it? The problem with the way I've formulated it above is that it looks like the Er of (genuine or mock) hesitation, synonymous with Um. In fact I think that would be as natural a reading of the sentence as the Yuck reading. This would significantly change the overall understanding, and change the response from disgust to something like confusion. I could try Err, but I don't think that's any less ambiguous. And of course I could write Yuck, which would convey the right sense, but direct quotation ought to respect the original wording. (I have a feeling that this is a British expression, so I'm tentatively tagging as BrE, but I'm uncertain about this. It's supported by noting that the answers to this question don't mention Er at all.)
Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my eyes during the run, I can really feel that I am moving. Now assume that I reach a world where there is absolutely nothing except my own body, and my eyes are closed. I am still feeling that I am running. The question is I am running wrt to what? Even if I open my eyes I would feel that I am still running, may be very fast. But visually I would not able to perceive my movement. Does it mean that my movement in space is an illusion? If not, then I am moving w.r.t what? There is absolutely nothing around me!
Or, I guess it could be worded, since when and why was it counted as part of a formal writing style to capitalize many general nouns? (After all, it's not German ...) This is also a trend in legal documents, however, I believe, attributable to the fact that certain terms (e.g. "Company") can have very specific definitions. Here is the second paragraph of the Declaration of Independence. We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.
One formulation of Dilworth's theorem(for finite partially ordered sets) states that : There exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. The above is an extract from this wiki page. However, I don't understand how the above statement is equivalent to the following formulation of the theorem. In any finite partially ordered set, the maximum number of elements in any antichain equals the minimum number of chains in any partition of the set into chains. The wiki article does try to explain this. Here is their explanation: Dilworth's theorem states that there exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. When this occurs, A must be the largest antichain in the order, for any antichain can have at most one element from each member of P. Similarly, P must be the smallest family of chains into which the order can be partitioned, for any partition into chains must have at least one chain per element of A. I don't get why the statements "...for any antichain can have at most one element from each member of P" and "....for any partition into chains must have at least one chain per element of A" together imply the maximality of the antichain and the minimality of the number of chains. Any help in understanding why these are equivalent formulations will be appreciated. Background: I am mostly a problem solver. I am learning order theory because of its connections to Hall's marriage lemma and because it seems very interesting. I am not following any book, but am trying to learn some order theory online. So I am a total beginner in this area.
I'm looking for the name of the logical fallacy where intent or agency is assumed when in fact there is none. It's a common fallacy in my experience, but I can't seem to find it described specifically on any site that discusses logical fallacies. It seems to be a special case of apophenia, but Wikipedia and Google turn up nothing specific to an "apophenia of intent" or any related phrase. The best I've been able to find is this rather obscure blog post that names it the "agency fallacy," but I haven't been able to find any other sites that use that phrase. Does this fallacy even have a name? Here are a few examples: A child, playing with magnets, finds that they repel when held one way and attract when held another way. Seeing this, the child thinks "oh, those ends want to be together, but the other ends want to be apart." They have (unconsciously) read intent into a deterministic physical process. A picnicker gets rained on and thinks "Darn it, rain! You just couldn't resist ruining a nice day, could you?" Again, they have (unconsciously) attributed agency to a mindless natural process. Two people pass each other in a crowded hall. One trips and stumbles into the other. The other thinks "What a jerk! Why'd they do that to me?" They have mistakenly attributed intent (specifically, malice) to an action that was accidental. This is the case of the fallacy that Hanlon's Razor warns against. A socialist on a soapbox shouts "Capitalism is the source of all the world's evil! It's stealing our jobs and lining the pockets of bureaucrats!" Although the use of metaphor is more deliberate here than with the child or the picnicker, it is still misleading: capitalism can't do anything on its own, only the people who participate in it can.
I was given the following question for comprehension pasted below: What does John mean when he says that he would only win his own money? And I answered that John meant that Marry won't be betting any money, so he will be winning only his own money. Professor marked it incorrect. Can you please what exactly is the problem? I have marked the relevant information in bold letters in the comprehension passage. "Hullo," said John, "it's raining again. What a nuisance I Now we shan't be able to play tennis this afternoon." "No," said Mary, "I suppose we shan't. Let's stay at home and stick some photographs in our book, shall we?" "Do you really want to?" said John rather doubt. fully. "I thought you said you didn't like doing it because it was so messy." "Oh,' replied Mary, "I'll just watch you sticking them in." "Oh, no, you won't," said John. "You've done that to me before. You'll have to do your share, my girl I " "All right. Then what about playing cards? You're keen enough on doing that with your friends at the club." "But you don't know how to play," protested John. "That's all right. You can teach me, can't you? You taught me to drive a car." "Well, it's not much fun teaching someone to play cards. The whole point of playing cards is the chance of winning." "You'd be sure to win if you played with me, because I don't know how to play. Surely that would be better than playing with your friends, because you sometimes lose there." "But if I did win when I was playing against you, I would only win my own money." Mary laughed. Then she said. "All right, I think we'll just have to go to the cinema. There's a good film on at the Grand, isn't there?" "Not the Grand," said John. "The Splendid." "Oh, yes," said Mary. "I keep on getting them mixed up. The Grand's the one down by the river, isn't it?" "Yes," answered John. "After we've been here a few more weeks we'll know everything there is to know about this town: it's small enough. Well, we'd better go, or we'll be too late for the matinee. Have you got your umbrella back from Jane yet, or will you have to go on sharing mine?" "No, I got mine back. I came across Jane in a shop this morning. She was carrying my umbrella, but she put it down for a moment while she looked in her handbag for some money. So I picked the umbrella up and started to walk out. The shopkeeper was horrified. He said, 'Madam, that umbrella belongs to this lady!' 'No, it doesn't,' I answered, 'it belongs to me.' 'That's right,' said Jane. 'It does.' You should have seen the shopkeeper's face! He didn't know whether to believe his eyes or his ears-especially as Jane pretended never to have seen me before: you know how she loves a joke!"
What are some good ways to motivate the material on infinite series that appears at the end of a typical American Calculus II course? My students in this course are generally from biochemistry, computer science, economics, business, and physics (with a few humanities folks taking the course for fun) - not just math majors. I have struggled some in the past to motivate the infinite series material to these students. For one, it doesn't fit with the rest of Calc II, which is on the integral. Over the years I have "converged" on telling them that the main point of the unit is Taylor series and that the rest of the material is there primarily so that we have the tools we need in order to understand Taylor series. Then I illustrate some of the many uses of Taylor series (mainly function approximation, at this level). This approach works better than anything I've come up with thus far with respect to getting my students to care about infinite series, but I feel a little like I'm selling the rest of the material short by subordinating it to Taylor series. Does anyone have other ways of motivating infinite series that they would like to share? (Again, only a small percentage of the students in my class are math majors.) Background: The material in this unit typically consists of sequences, basic series (like geometric and telescoping ones), a slew of tests for convergence (e.g., integral test, ratio test, root test), an introduction to power series, Taylor and Maclaurin series, and maybe binomial series.
I am a pre-engineering student currently taking a Single Variable Calculus course at a community college. I recognize that my future success (or not so much) as an engineer will be based, in large part, on my capabilities with and understanding of Calculus. Therefore, I really, really want to master it like I've never mastered any subject before. I'm doing well in my class, and my instructor is great, but I am under the impression that this course and it's textbook (Calculus, Early Transcendentals by Stewart) do not delve quite as deeply into Calculus as I would like. Also, the textbook frequently introduces new techniques and concepts with little to no explanation. (Incidentally, I'm a self-taught software developer, so I am adept at learning new topics on my own. Learning Mathematics is, IMHO, quite similar to learning a new programming language.) So I'm hoping to find some really excellent Calculus textbooks that will give me deep insight into the topics of differentiation and integration (and any other topics my course may be missing). I've used Google and my school's library to search extensively, and I've found no shortage of Calculus textbooks. My problem is that, since I'm just now learning the basics, I have no way to know just how in-depth an advanced or in-depth book should go, or what important information my current textbook may be missing. I own a copy of The Calculus Lifesaver, by Adrian Banner, which is absolutely outstanding. If anyone reading this happens to be struggling with Calculus, this is the book to turn to. I also have been taking advantage of the Calculus courses in MIT's OpenCourseware. Calculus Revisited, with Herbert Gross, has been very helpful. His way of explaining the concepts just really "clicks" with me. So, with that said, I'm just hoping the experts in the community here can recommend some great resources (e.g. books, free online courses, or other media) to help me optimize my knowledge of Calculus. Thanks in advance!
I am new to the world of stochastic processes and Brownian motion, and am having a hard time finding easily digestible reference material (especially ones with well-worked out examples). So, in a way this question is more of a request for sources/references than a specific answer. To give a little context to where I am approaching this from, it is specifically from the class of statistics referred to as "group sequential testing" (though there are several similar or analagous names, such as "interm analyses", "conditional power calculations", "futility analyses", etc.). I am posting this here rather than on CrossValidated simply because cursory searches reveal that people here are more familiar with the basics of stochastic processes than seems to be the case over on the stats-specific StackExchange, so I feel that I will get more helpful advice/answers here. Anyway, the primary textbook for this field of statistical analyses is Statistical Monitoring of Clinical Trials: A Unified Approach, by Proschan, Lan, and Wittes. The basic mathematical framework for much of the book is Brownian motion; that is, the theory behind many of the group sequential tests outlined in the book is founded on the fact that standardized test statistics evaluated over time can be seen to satisfy the properties of Brownian motion. What I am trying to do is prove whether or not certain classes of non-parametric statistics (specifically the Wilcoxon rank-sum) satisfy these properties, and thus allow one to use this broader framework in that context. So, what I am looking for are sources or references with examples of demonstrating how some arbitrary process can be shown to satisfy the properties of Brownian motion. When I search this site or Google, I can find dozens of examples, but none of them are quite that helpful, since the are generally all based on proving that some function of a Weiner process is itself a Weiner process (e.g. this question or this one). These aren't terribly illustrative to me, since the proofs all rely on the fact that some element of the process under consideration is already given to satisfy the properties of Brownian motion, rather than "starting from scratch", so to speak. Now, I do know the basic steps for proving a process is Brownian motion (this question has them delineated rather nicely). However, I am having a difficult time finding any worked examples of these steps being applied to a process "from scratch" (which is especially critical since I am unfamiliar with a lot of the notations used in stochastic processes, which are often subtly different than those taught to us statisticians). Can anybody point me in the direction of some nice examples or references that would be helpful, here?
There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you move the molecules from cell to adjacent cell at random, the large-scale results are in many ways a good simulation of gas behavior. In particular, even though molecules are individually moving in only the four cardinal directions, at a large scale the simulation does not show any bias to these four directions. If you start with a large square lump of material, it will rapidly diffuse into a circle. This property of the simulation is called isotropy. Long ago when I was involved in research in this area I was told that this worked fine for gas flow simulations, but not for incompressible fluids. If one wanted to make an isotropic two-dimensional simulation of incompressible fluid flow, I was told, one had to use a hexagonal lattice instead of a square lattice. I was told that one could deduce from the Navier-Stokes equations that that any simulation of incompressible fluid on a square lattice would necessarily be anisotropic. Is this correct? If so, how does the proof go? If the argument is complex, is it possible to get an intuitive idea of why compressible and incompressible fluids are different in this regard? What is a reference that would include the full proof? Addendum: Despite the answer I posted below, I still don't understand any of the details. I would be glad to award the bounty to someone who could explain it.