Find location of bash command binary file I have a command letsencrypt which I use in the terminal.  I tried to find the binary via grep -R "letsencrypt" /. Not a good idea, some sort of loop was invoked.  Is there a simple command to see what the command letsencrypt actually invokes for binary?
Shell command for outputting absolute path of binary Is there a shell command for outputing absolute path for specified program? I'd like to know where executable binary file is.
What is the purpose of  in Python — especially with respect to when I would want to use it, and when not? Let $f:S^{2n} \rightarrow S^{2n}$ be a continuous map. Show that          there exists $x \in S^{2n}$, such that $f(x) =x$ or $f(x) = -x$;   any continous map $g: \mathbb R P^{2n} \rightarrow \mathbb RP^{2n}$ has a fixed point;      I think 1 implies 2. So, how can I find an $x$ in 1?  Thanks for the help. "None" as plural indefinite pronoun In my grammar book (English Grammar, HarperCollins Publishers), I read that none is occasionally treated as plural, but it is usually regarded as singular. Can you give me an example of sentence where none is used as plural pronoun? Evaluate the integral $$\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$$ Show badges in user profile in iOS app When viewing a user's profile from the iOS app, it would be nice to be able to see what badges they have, instead of just the counts. Evaluate $$I=\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$$   I try to change it to:$$I=\int_{0}^{1}\frac{(1-x)\log(1-x)}{\log x}dx$$ but I can't do next steps,help me ,thank you very much. Strange OutOfMemory issue while loading an image to a Bitmap object How to randomly subset X% of selected points? Notification for reviews shows way too many Since a , I see more than I should:    I see no reason to see 134 posts are awaiting review, when there is literally nothing I can do about them. I think it is a bug, because notification is meant as something that will make me act. When I know I usually can't, obviously I will start to ignore it.  If it's not a bug, please remove bug tag and explain how it is supposed to be useful, or how can I switch to only seeing notifications about things I can act on.  Note that apaprently there are no flags for me, neither. I see only stats, migrated, close, delete, there, as if there was no flags waiting:    If you expect us to click on it every few minutes  just to see personalized numbers next to queues, why don't you simply query for personalized numbers every few minutes and cache them for us? It should cost you similar, in database usage, and will save us a lot of clicking and frustration.  If all this number means is "there might be reviews, or not" or "for sure there are none"  it would be simpler just to hide "review" link in the second case. We don't need two links with the same function next to each other, thank you, one is enough, and meaningless numbers are only irritating. According to :     The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent.   Does point particle mean the particle should not have a shape, surface area or volume?  But when I searched Google for the "electron shape" I got many results (like  and ) that says electrons are round in shape. How do you find the transfer function of a controller? Below is a block diagram of the system. I thought the circle symbol with the plus and minus sign was an op-amp but I'm not sure whether that's the case. I want to find the closed loop transfer function. If there was no feedback (open loop), then I think I could find the output as Y(s) = Vin*G. This would mean that the transfer function is Y(s)/Vin = G.  Any ideas for how to find the closed loop transfer function and what the circle means? Repeating the consonant in many words in a sentence or phrase In the movie 'V for Vendetta' you have for example (bold part):     Evey: Who are you?        V. : Who? Who is but the form following the function of what and what I am is a man in a mask.      Evey: Well I can see that.        V. : Of course you can, I’m not questioning your powers of observation, I’m merely remarking upon the paradox of asking a masked man who he is.      Evey: Oh, right.      V. : But on this most auspicious of nights, permit me then, in lieu of the more commonplace soubriquet, to suggest the character of this dramatis persona.      V. : Voila!   In view humble vaudevillian veteran, cast vicariously as both victim and villain by the vicissitudes of fate. This visage, no mere veneer of vanity, is a vestige of   the “vox populi” now vacant, vanished. However, this valorous visitation of a bygone vexation stands vivified, and has vowed to vanquish these venal and virulent vermin, van guarding vice and vouchsafing the violently vicious and voracious violation of volition. The only verdict is vengeance; a vendetta, held as a votive not in vain, for the value and veracity of such shall one day vindicate the vigilant and the virtuous. Verily this vichyssoise of verbiage veers most verbose, so let me simply add that it’s my very good   honour to meet you and you may call me V.       Evey: Are you like a crazy person?      V. : I’m quite sure they will say so.   What do you call sentences like these? And do you know some other ones? Ubuntu 20.04 run ok on Lenovo ThinkPad E15 laptop? Integral of Sinc Function Squared Over The Real Line I am trying to evaluate $$\int_{-\infty}^{\infty} \frac{\sin(x)^2}{x^2} dx $$ Would a contour work? I have tried using a contour but had no success. Thanks.  Edit: About 5 minutes after posting this question I suddenly realised how to solve it. Therefore, sorry about that. But thanks for all the answers anyways. what's different between each and collect method in Ruby Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company...  Now someone (or some formula) comes along and says "let's take/use the log of the distribution" and here's where I go WHY?  Questions:   WHY should one take the log of the distribution in the first place? WHAT does the log of the distribution 'give/simplify' that the original distribution couldn't/didn't? Is the log transformation 'lossless'? I.e., when transforming to log-space and analyzing the data, do the same conclusions hold for the original distribution? How come? And lastly WHEN to take the log of the distribution? Under what conditions does one decide to do this?   I've really wanted to understand log-based distributions (for example lognormal) but I never understood the when/why aspects - i.e., the log of the distribution is a normal distribution, so what? What does that even tell and me and why bother? Hence the question!  UPDATE: As per @whuber's comment I looked at the posts and for some reason I do understand the use of log transforms and their application in linear regression, since you can draw a relation between the independent variable and the log of the dependent variable. However, my question is generic in the sense of analyzing the distribution itself - there is no relation per se that I can conclude to help understand the reason of taking logs to analyze a distribution. I hope I'm making sense :-/  In regression analysis you do have constraints on the type/fit/distribution of the data and you can transform it and define a relation between the independent and (not transformed) dependent variable. But when/why would one do that for a distribution in isolation where constraints of type/fit/distribution are not necessarily applicable in a framework (like regression). I hope the clarification makes things more clear than confusing :)  This question deserves a clear answer as to "WHY and WHEN" What are those characteristics by which every sound can be identified uniquely? Java socket/serialization, object won't update Let $f$ be a holomorphic function defined on $\Bbb C$ such that $f^{-1}(\Bbb R)=\Bbb R$. Prove that there exists $a,b \in \Bbb R, \; a \neq 0 \;$ such that $f(z)=az+b \;$ for every $z \in \Bbb C$.  I was given a hint: define the function $g(z)=\frac{f(z)-f(0)}{z}$. such $g$ is also holomorphic in $\Bbb C$ since the only singularity is in $0$, and it is a removable singularity since we can define $g(0)=f'(0)$. Next I thought about proving $g$ is bounded, and thus constant (using Liouville's theorem), but pretty much out of ideas. How can I finish the proof/solve in another way? A financial planner treated us in a dismissive fashion and I want to say that he "gave us the back of his hand" but that phrase doesn't seem to have the meaning of dismissive. Does it or is there a similar idiom?