preferred_anon

Mar 14 20:41
@HamoodAli I think Euler's approach "fits into modern mathematics" by "being the same thing as the integral test". Any further distinction is too subtle for me to understand.
Mar 14 20:41
@HamoodAli I have a couple of problems with the new question. First of all, I think you've changed the character of the question significantly, and it would be better to ask a new question in this case. The new question seems to be about historical context ("how did Euler think about this") which would be better suited to the History of Science & Math stack. I can't really see how your idea is any different to the integral test for convergence. I am worried that the answer you need is "read an understand the proof".
Mar 14 20:41
This stuff about integrals having more terms and therefore being bigger is not meaningful. Even a sum with one term can exceed an integral with "infinitely many terms". An integral is a limit of finite sums, but that says nothing at all about how big the limiting value is.
 
Mar 13 19:48
Why do you distinguish between "direction purposes" and "mathematical operations"? It is a perfectly mathematical question to ask "what direction does this vector point in?" for example.
 
Nov 27, 2024 14:09
The readme and license are not relevant for whether you may access the servers that the software uses. One mechanism for access control is a contract. In the absence of a contract, the server owner may use technical means (rate limiting, authentication, etc), and circumventing that could count as hacking by some legal definitions. In the absence of a contract or technical restrictions, there is no limitation on your use of a public server. So I think the impression of a legal landmine for using free software is wrong. But if you're not satisfied by that, Law.SE is available.
 
Nov 18, 2024 20:21
@gerrit bus factor 1 does not usually mean "worth many times your salary", I think. It only means the team would be slowed down significantly by your absence -- perhaps in a huge company that might mean being worth double your salary temporarily, but I think that is quite rare
 
Oct 3, 2024 13:51
No, this is not a proof. This statement is a counterexample to "for all $x, \cos x + \sin x < 1$". The statement to be proved is "for all $x, \cos x +\sin x \ge 1$", which cannot be proved by counterexample. You can only prove existence statements by (counter)example.
 
Jul 24, 2024 20:38
@DmitryGrigoryev I am not sure why it would be bad faith. Hilmar says "Quite likely it has nothing to do with race", but I don't see any reason to conclude this any more than for anyone else. In other words, merely that racism is unlikely on average does not mean that racism is unlikely in this case, relative to other cases. I actually think it a plausible explanation, even though alternative explanations are possible.
 
Jun 16, 2024 00:55
@Koschi fictitious forces are pretty much exactly what you describe If you accelerate a body in a circle, it will "cause" a "force" in the sense any reasonable person could mean it (i.e. you feel something pushing on you)
 
Jun 14, 2024 14:47
@DanRomik I'm surprised! I can't think of any industry where this would be acceptable behaviour. Retracting an acceptance is just unconditionally bad manners IMO.
Jun 14, 2024 14:47
Indeed, I don't think OP's question is really about Academia per se. Everybody looking for a job has to make the same sort of choice.
 
May 23, 2024 22:26
Saying "he's my always" is not the same as saying "he's mine always" or any other "proper" sentence that captures an aspect of the meaning. There is a certain sense about choosing words that aren't typically grammatical that is not captured by turning it into a grammatical sentence in another language.
May 23, 2024 22:26
Like it or not, "it's obvious to a native speaker" is just as valid a claim as "it's obviously wrong to a native speaker" (and I think both are true). The point is that translating it into "proper English" ("normal English" if you prefer?) loses the sense of the quote.
May 23, 2024 22:21
@IMSoP I know you don't like it, but it is true (or, if you prefer, obvious to a native speaker), and it is relevant.
May 23, 2024 22:21
@IMSoP Of course it is. But that conversion is cultural and not universal, so just translating it is not going to preserve the original sense. It's like translating "I steamrolled him". You either preserve the words (and end up with gibberish) or preserve the meaning ("I ignored what he said") but you can't preserve the words and the meaning and the idiomatic nature of the sentence.
May 23, 2024 22:21
You probably don't want a translation, because the sentences you give aren't proper English. Are you sure you don't just want an idiomatic expression of love in Latin?
 
May 1, 2024 16:01
@Traveller I don't think any of that contradicts the fact that you are implicitly excusing the officer's behaviour by suggesting the commenter should have addressed them differently. Putting aside whether I agree with you HO, "they might see [innocent chit-chat] as a clumsy ruse" is an excuse, and telling someone who has been abused that they could have avoided the abuse if they behaved differently is dictionary-definition victim blaming.
May 1, 2024 11:24
@Traveller "Not making excuses or blaming the victim" - yes, you are. Saying that the conversation "should be adjusted to the cultural norms" means that you consider those cultural norms acceptable. Otherwise, you would not accept them. If your remark is merely intended as "advice for your safety" or similar, avoid words like "appropriate", which come with a normative connotation.
 
Apr 25, 2024 16:48
@FShrike The top voted answer says "This means that not only can the output of a function be a set, it actually must be. In set-theoretic mathematics, nothing exists except sets, so everything that exists is one."
Apr 25, 2024 12:55
Isn't this question more appropriate for Math.SE?
 
Nov 30, 2023 13:37
This conclusion is entirely consistent with the Iraqi statement in the answer. Yes, this act is evil. It is in response to other evil acts. There have been many egregious evil acts in both directions for a long time. It doesn't matter who is in the right. All that matters is what further actions advance peace, and what actions hinder it. The actions of Hamas hinder it. The retaliation of Israel hinders it. Asking "who is the goodest murderer" hinders it.
2
Nov 30, 2023 13:32
Indeed, we are far beyond the point where naive morality would or could apply. If you discover that A has murdered B's entire family, and B responds by murdering half of A's family, who is in the right? What if the murders have gone back and forth for ten generations? What if some of the murders involved torture? If you take the situation in its totality there is no simple conclusion to draw. Evil has been done, and we must do whatever is necessary to stop it.
Nov 30, 2023 13:28
But in this context, where the action is so transparently evil, I think it has a different interpretation. Namely, that if you put a person in extreme, inhumane conditions, then it is likely that person will act in an extreme, inhumane manner. It is easy to dismiss this from a position of comfort, and certainly there have been people in history whom have endured the most inhumane conditions imaginable and chosen not to behave in the same manner.
Nov 30, 2023 13:26
ugh, posted by accident. I guess I'll try to finish
Nov 30, 2023 13:26
I agree with Evan's position completely and I think I can phrase it in different words. Certainly some people use "natural" as a normative statement. "It would only be natural to X" often means the person considers X to be a reasonable, sensible, good, whatever you like. But in this context,
 
Oct 7, 2023 21:48
@NotThatGuy There is no contradiction there. The law states that any accommodations in a certain general category must be provided. Since neither Bob nor Alice has perfect knowledge of what the job will entail in the future, nobody knows exactly how much that will cost. Perhaps I should have said "Since nobody knows the dollar value of those accommodations".

No assumptions at all are required to say that Alice has to comply with the law, and thus estimate the cost of that compliance. In the alternative case, where the law doesn't apply, Alice only has to estimate what costs she is prepared
Oct 6, 2023 20:09
Ugh, "enter" sends the message. I wasn't done.

The claim is that since the law is not precise about what accommodations are required, Alice is required to guess (or pay) to determine what they are. It's entirely possible that either her estimate of that burden, or the cost to attain its value, are more than the cost of the actual accommodation Bob requires.

In that case, the law would have caused Bob not to be hired, even though Alice actually has the means to hire him, and the will to accommodate for him.
Oct 6, 2023 20:04
@NotThatGuy RE "Alice might do good things ... if there is no enforcing it ... but if there's a law, she's instead discriminate against Bob." - since the argument is about providing accommodations, it's clearer to phrase it in those terms. The claim is that Alice might provide some accommodations if there is no law. If there is a law, she must either provide all accommodations specified by the law, or none (by not hiring Bob at all).
 
Aug 23, 2023 17:09
@jcaron Well, then I don't think I understand your comment well at all. The premise of the question is that one is skipping the B-C leg to save money. If missing the flight does not save money, then any rational person would take the cheaper flight. A case where A-B-C is cheaper than A-B may be rare (you'd hope so!), but it clearly exists, or Skiplagged would never have existed in the first place.
Aug 23, 2023 17:09
@jcaron I don't think anyone is comparing A-B-C flights with A-C flights. As you say, cutting out an intermediate destination has actual value and is legitimate to charge for. By contrast, Hilmar compares an A-B-C flight with an A-B flight, where there is no difference whatsoever for the passenger travelling to B. Charging more for a service which transparently requires less work due to an arrangement you have with a third party is profoundly unintuitive for a customer who has no visibility or control over those agreements, and some commenters seem to consider it unethical.
 
Jul 28, 2023 05:53
@JonathanReez Oh the very first graph. I thought you meant the first graph among the three that SirHawrk refers to. "efficiency" is not a particularly meaningful concept when considering government programs, since they tend to perform services that nobody in the private sector is willing to do. But it would probably waste everyone's time to argue about it here.
Jul 28, 2023 05:53
@JonathanReez I'm struggling to understand your comment. Do you consider it a bad thing that 40% of the "productivity" (I guess you mean GDP?) is spent on government programs? Do any of the graphs show that, or is that an unrelated statistic? What makes the first graph worse in your opinion?
 
May 16, 2023 09:08
@jpa It is not so much that copyright interpretation is stricter in programming, as much as it is that it's harder to write a program that does that same thing without copying. To write a book with "feature-parity" with an existing one still leaves one with a lot of freedom in how to construct it, but with software you are more constrained.
 
Mar 27, 2023 10:49
@MelodySkirata I was in a similar position myself a couple of years ago. If you're interested in political change in this direction, I encourage you to look up the Free Culture movement. There is a large minority of people who would like to see the copyright system changed to enable this kind of harmless/prosocial sharing. But that's offtopic on this stack. (by the way, it's not just US copyright law - copyright is pretty much the most internationalised legal scheme we have)
Mar 27, 2023 10:49
@MelodySkirata No, that is typically not legal.
Mar 27, 2023 10:49
I seriously doubt that the ToS is relevant here. This would imply that merely browsing any internet site lacking a ToS would be an infringement by default. It seems the same argument would apply to images - where in most cases the downloading is a completely involuntary part of browsing the web. Consider, for example, this question which addresses the problem of caching content more generally. In particular, the note that "local browser caching is fair use".
 
Feb 2, 2023 01:21
 
Jan 24, 2023 08:35
I don't see why P(H) should not increase. If it is possible at all that monster is causing you to see heads, and you see heads, doesn't that make it slightly more credulous than before that this is the state of affairs you're in? If you get a million heads in a row, would you reconsider again? It seems like your mistake is assigning a very low positive probability to something you really consider impossible, so that very low probability possible events may seem likely by comparison. There is no problem here from a Bayesian perspective, IMO.
 
Nov 22, 2022 08:42
Are you sure you want to support old browsers, and not just minimalist ones? I have in mind things like Lynx, which support modern protocols, but not things like JS.
 
Nov 15, 2022 20:33
If you are interested in games without this property, consider supporting your local open source game developer.
 
Oct 16, 2022 06:18
I think boring openness is probably the simplest way out of this issue. But I doubt your claim that people will think it "very rude" not to want to discuss your accent. This is obviously culture-dependent, but where I am from it is not uncommon for the questioner to be considered very rude for asking where someone is from based on their accent.
 
Sep 25, 2022 22:39
@DavidSchwartz You seem to be conflating the utility to the firm of the case study with its market price (were it to be sold). The firm gets utility from the case study only if it is not widely available. That does not incentivise them to produce more - it incentivises them to keep them secret. If we assume the case studies are never shared (as the firm's actions intend) then the aim I stated can never be satisfied by definition (there is no need to incentivise people to produce works that only they themselves will ever use).
Sep 25, 2022 22:39
@DavidSchwartz higher value works only encourage production if your aim is to sell them. No doubt the firm would be economically better off if they can enforce trade secrecy in this way - they spend less time producing resources. But precisely because they spend less time producing resources, there are less resources produced.
Sep 25, 2022 22:39
The legal question here is obvious. However, it is worth noting that unless the firm itself intends to sell the case studies, this appears to go directly against the stated aim of copyright law (the encouragement of the production of creative works).
 
Sep 20, 2022 08:00
@ItalianPhilosophers4Monica Woah there, buddy. It's off-topic and the mods will probably delete this thread, but I'll bite. Every Elon Musk project is either viable or original, and there is no overlap. Teslas will never self-drive (they have admitted this). The hyperloop is a century old failed project. Reusable rockets are not new. The solar roofs demo was a fake. There are no tesla robots. There is no tesla semi. The list goes on.
Sep 20, 2022 08:00
I don't think it does your answer any good to quote Musk and then simply "dismiss it as Musk-speak". Why quote a fraudster in support of your point? (a list of his exaggerations and lies would be too large for this comment). It does at least touch on a major reason for success in a lot of large private companies - they get private profit at substantial public expense.
 
Jul 22, 2022 08:22
@gerrit Note that the quoted argument is only suggested in the short-term, when the neighbourhood is transitioning from low density to high, and is probably underserved by the existing services in the area. Of course, the increase in services might "get ahead" of the increase in pop density, so you may still disagree, but it is not like-for-like to apply that argument to already high-density areas.
 
Jun 30, 2022 20:15
@Someone RE: "A foreign court ruling is "due process of law" in the United States?" What do you think would happen if you committed an ordinary crime in a foreign country? Not every ruling would be respected, but most would.
 
May 1, 2022 03:11
I downvoted - this answer makes no attempt to explain why published contributions would require co-authorship, which (if it is the intended argument) is patently absurd. Should Einstein be a co-author on every GR paper, because it uses his equations? Of course not. If there is a more subtle argument, it isn't apparent in the answer or the comments.
 
Mar 20, 2022 17:00
Depends on your axioms. A classic definition of the reals in pure set theory is in terms of inductive sets (as a subset of the entire universe, not just the reals). Depending on how Munkres defines reals, defining the integers in terms of them could be circular. It's probably just done to give you tangential exposure to inductive sets as a concept. But I've not read the book.