Trivial parsec example produces a type error
What is the monomorphism restriction?
Shuffling questions in exam This morning, I read Wikipedia's informal definition of a limit:     Informally, a function f assigns an output $f(x)$ to every input $x$. The   function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever   $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$   as $x$ moves closer and closer to $p$.   To me that sounds like something that might be better described as a 'target'.  If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).   So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.   What is a simple example of a limit in the real world?  Thank you  -Hal. Do fixtures trigger model callbacks? External Hard Drive no longer working I am on a MacBook Pro 13 running latest Sierra. I have an external Seagate solid state hard drive that was working and out of the blue stopped working. The only thing on it was my Adobe Lightroom images/videos. Not the LR DB files. I'm sure you have all heard this woe before, so I won't dwell on that. And yes, I back up to the cloud. AWS S3 specifically. Though I am traveling South East Asia for the last year, and staying in cheap hostels. So good internet is hard to come by sometimes. I can't back it up after every export. While most of it is backed up, there is some that is not.  Moving on. The symptoms seems to change every time I plug it in. The first sign was it ejected on it's own. I plugged it in again, and it wouldn't mount. Disk Utility recognized it, so did the command line diskutil list but it wouldn't mount. I rebooted and it worked for a second. Then I could only get to it from the command line. Then trying to frantically back up to my local what was not backed up to the cloud, it all failed. Basically just a cp -R [directory] [local-directory] command.  After some more frantic unplugging and re-plugging plus some command line manual mounts, I finally got it to where the Disk Utility would be able to run first aid on it. It failed. I don't recall the error. So I put it in a freezer. After a few hours I tried again. It is not any better. It still will not mount. Now Disk Utility sees it, but with no partition. I can't even give me information about how much space is used on it.  I have also tried it from a Windows machine. It did not mount. I have tried other cables. No success. As well as tried my other USB port. I also have another working external hard drive exactly like the one giving me issues. It works on all cables and USB ports.  I do have Docker running with a Ubuntu container, I'm trying to think of a way to see if I can try to get to the USB from there. I also have a USB that I have thought about running a live Ubuntu on there to see if I can mount and retrieve the data or fix the HDD that way. But if it will not mount, I doubt these will work.  Can anyone else think of any other tricks I can try myself to see if I can repair this or at least retrieve the data without paying for a service or software? If not, those suggestions are also welcome.  Update   I made the mistake in original post that it was a Solid State Drive. This is my mistake, it is actually a spinning disk hard drive. I bought them long ago and have been traveling with them for so long I just forgot. Question is updated to reflect this. Now diskutil list does not show it at all. The Disk Utility app also does not see it. Based on suggestion from @Allen I seeked out the USB to SATA cable. I did not quite find it, as my options are extremely limited where I am at. Though a local expat on a facebook group was able to help me with a empty 2.5 casing that I was able to extract the drive from original casing and put it in his blank case. It now mounts. Though it has the "click of death" sound to it. And data is not really reachable. While I can ls the directories and Adobe Lightroom does not have the exclamation mark when it can not reach the actual external files. Right clicking on the images and clicking on "Show in Finder" or any other variation of trying to get to the files through Finder or terminal, I have no success. It usually hangs and I get the spinning wheel. Since Adobe Lightroom imports these images into directories named by date, I am going to send the drive off to a data recovery service and ask to recover just unbacked up directories i.e. dates. Next time I will make harder efforts to backup and probably get an actual SSD.   I think this can be closed, due to my low reputation points I can not close this myself. How to change maximum number of cores? It says in  that there is a maximum number of 8 cores supported by default in Ubuntu 12.04 Desktop/Server 32-Bit. What is the way to increase the maximum number of cores from the default of 8 to a higher value, like 12?  The reason I ask is because I have just built a machine with 6 hyper threading cores.  There were issues installing the 64-bit version of the software from a CD (it "panicked" and crashed several times).  The 32-bit installed with no problem, but I only see 8 of the 12 cores.  The BIOS is fine.  If I turn hyper-threading off and reboot, I see 6 cores as expected.  I am nervous to try and compile a kernal, I am still new to all of this.  Is there a config setting somewhere that I should change? When "Questions that may already have your answer" (similar questions) appear as a right column, it overflows and overlaps the footer.  (shown in the figure)        This happens on all SE network sites on which I have asked questions.  Also this happens to other columns also like "How to Format". Produce an explicit bijection between rationals and naturals? What is the difference between fixed effect, random effect and mixed effect models? In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models? Assign default keyboard language per-application Is it possible to assign default keyboard language for specific applications? I know that there is an option to always start an application with a default keyboard language but this is not what I want.  I'm looking for something similar to "fixed workspaces" which you can set using CompizConfig (You set Chrome to always open at X1Y1, terminal at X2Y1 etc). Something where I would set Chrome: Czech, terminal: English, Spotify: English, ... I'd like to make commands I've typed (input) into terminal stand out from all the output.   For example:  imac:~ buster$ chmod -R g-w myfolder  imac:~ buster$ cd myfolder imac:myfolder buster$ ls -l total 0 drwxr-xr-x   9 root  admin   306 Apr 20  2010 bin drwxr-xr-x   7 root  admin   238 Apr 20  2010 include drwxr-xr-x  73 root  admin  2482 May 18 17:16 lib drwxr-xr-x   6 root  admin   204 Apr 20  2010 man imac:myfolder buster$ echo Go Giants! Go Giants!  bold jumps to mind but I'd accept a color or even highlighting the whole line...   I'm sure there's a way to do this but it's not obvious to me...  thanks! Javascript add js libraries by code I'm fitting a regression on the $\log(y)$.  Is it valid to back transform point estimates (and confidence/prediction intervals) by exponentiation?  I don't believe so, since $E[f(X)] \ne f(E[X])$ but wanted other's opinions.  My example below shows conflicts with back transforming (.239 vs .219).  set.seed(123)  a=-5 b=2  x=runif(100,0,1) y=exp(a*x+b+rnorm(100,0,.2)) # plot(x,y)  ### NLS Fit f &lt;- function(x,a,b) {exp(a*x+b)}  fit &lt;- nls(y ~ exp(a*x+b),  start = c(a=-10, b=15))  co=coef(fit) # curve(f(x=x, a=co[1], b=co[2]), add = TRUE,col=2,lwd=1.2)  predict(fit,newdata=data.frame(x=.7)) [1] 0.2393773  ### LM Fit # plot(x,log(y)) # abline(lm(log(y)~x),col=2) fit=lm(log(y)~x) temp=predict(fit,newdata=data.frame(x=.7),interval='prediction') exp(temp)         fit       lwr       upr 1 0.2199471 0.1492762 0.3240752 Linux ACL behaviour: settings the mask changes 'ls' output, but not actual permissions It might be the time of night, but this is puzzling me. Picture the following.  [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x  3 root root     4096 Feb  9 21:53 . drwxr-xr-x 25 root root     4096 Feb  9 21:54 .. drwxr-x---  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# setfacl -m m::rwx foo [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x mask::rwx other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x   3 root root     4096 Feb  9 21:53 . drwxr-xr-x  25 root root     4096 Feb  9 21:54 .. drwxrwx---+  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# su - testuser [testuser@node1 ~]$ cd /acltest/foo/ [testuser@node1 foo]$ ls -la . total 16 drwxrwx---+ 2 root testuser 4096 Feb  9 21:53 . drwxr-xr-x  3 root root     4096 Feb  9 21:53 .. [testuser@node1 foo]$ touch bar touch: cannot touch `bar': Permission denied   In words: I create a directory foo, with mode 0750, root as owner and testuser as the group. (testuser is the private group of testuser, but that doesn't matter.)  The getfacl command correctly shows no ACL's on this directory and there is not mask yet. The mask will be set accordingly to the group permissions if I would add a named group or user now.  If I explicitly set the mask to rwx now, the group permissions as shown by ls change too. I know it happens the other way around (the mask changes when the group permissions change), but this seems puzzling.  The more puzzling because the getfacl output does not show the group permissions as rwx but - as said - ls does.  Which one is right? Apparently, the output of getfacl is right, because testuser cannot write to foo. As expected, by the way, because I did not grant the testuser group any permissions to do so.  It goes on. I cannot allow the testuser group write permissions on foo by just using chmod. I have to explicitly set an ACL using setfacl -m g:testuser:rwx foo to allow testuser to finally touch foo/bar.   Can someone explain the rationale behind the difference in the outputs of getfacl and ls? I know it can be tricky to have normal permissions go together with ACL's, but this seems plain wrong. (Though I expect to be missing something glaringly obvious ;))  I have already seen While executing a C program, a.out, using the Ubuntu terminal, why do I always need to type ./ before a.out, instead of just writing a.out? Is there solution for this? is the group of rational numbers the fundamental group of some space? Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics? In classical mechanics, we had Newton's law of gravity $F \propto \frac{Mm}{r^2}$.  Because of this, all laws of classical electrostatics applied to classical gravity if we assumed that all charges attracted each other due to Coulomb's law being analogous.  We can "tweak" classical electrostatics to fit gravity.  In modern physics, does the reverse work?  Can we "tweak" General Relativity to accurately describe electrostatics or even electromagnetism? If an opponent casts  to gain control of  then sacrifices it who will draw the card? I have a requirement where a certain field can be edited without the validations firing for a particular user. Now I tried to write rule like LastModifiedId != '005000000000000AAA' but the validation was still firing. Then I realized that until the record saves, the LastModifiedId does not change and the validations still fire, as the LastModifiedId would not be updated to the exempted User.   Is there any workaround or a way to check the Id of the User who is currently editing the record? Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$ I have to show the inequality of $$\left(\sum_{i=1}^n x_i\right)*\left(\sum_{i=1}^n \frac{1}{x_i}\right) \geq n^2.$$For $x_1, ... x_n \in \mathbb{R_{&gt;0}}$ and $ n \geq 1$. I wanted to show this inequality by induction. The basis is clear, but I am not sure how to do the inductive step. Can someone help me with that? Comment font sizes are inconsistent on Android An issue similar to that described in  and likely to be related.  The comments for a question may vary in size:         Chrome for Android on Nexus 7 running 4.2.2 Jelly Bean. This also occurs on Firefox for Android: