FFmpeg remove video frames at specific intervals
Selecting one every n frames from a video using ffmpeg
How can a function with a hole (removable discontinuity) equal a function with no hole? I've done some research, and I'm hoping someone can check me. My question was this:  Assume I have the function $f(x) = \frac{(x-3)(x+2)}{(x-3)}$, so it has removable discontinuity at $x = 3$. We remove that discontinuity with algebra: $f(x) = \frac{(x-3)(x+2)}{(x-3)} = (x+2)$. BUT, the graph of the first function has a hole at $x = 3$, and the graph of the second function is continuous everywhere. How can they be "equal" if one has a hole and the other does not?  I think that this is the answer:   Because the original function is undefined at the point $x = 3$, we have to restrict the domain to $\mathbb{R} \setminus 3$. And when we manipulate that function with algebra, the final result, $f(x) = (x + 2)$ is still using this restricted domain. So even though the function $f(x) = (x+2)$ would not have a hole if the domain were all of $\mathbb{R}$, we are sort of "imposing" a hole at $x = 3$ by continuing to throw that point out of the domain.   And then just to close the loop: Removing the removable discontinuity is useful because it allows us to "pretend" that we're working with a function that is everywhere continuous, which helps us easily find the limit. But the reality is that the function $f(x) = (x +2)$ is actually NOT continuous everywhere when we restrict the domain by throwing out the point 3. Or am I now taking things too far?   Thanks in advance!  EDIT: For anyone coming across this in the future, in addition to the excellent answers below, I also found this other question about the  helpful. Connect to Linux by name rather than IP I use VirtualBox on my MBP and often need to mount my USB flash drive inside the guest.  The problem I'm running into is that the host OS (OS X Mavericks) immediately mounts the USB flash drive when I insert it.  When I try to unmount it (gracefully, through Finder), OS X complains that the device is in use.  Further research into lsof reveals that Spotlight and AVG are doing their thing with the flash drive.  Rather than fiddling with individual app settings, I'd like to just modify the host OS behavior so that the USB device doesn't auto-mount.  Any suggestions? AES plaintext is smaller than 128 bits - how to expand? We are currently developing a little AES implementation in a crypto-course at university.  As far as I know, AES uses a 128 bit block length, so all data that will be encrypted gets split up into blocks of 128 bits (16 bytes) into a 2d-array (or 1d in implementation) with 4 &times; 4 fields.  I was wondering and didn't find out what to do if the entered string to encrypt is not 128 bits long? The question is going further by thinking that there will never be exactly n &times; 128 bits of data to encrypt.  For a smaller key given by the user (e.g. "test") I know there is a key expansion algorithm defined.  But what should be done for data that is less than 128 bits? Which metric to use to evaluate highly imbalance classification model performance I have to do classification model to predict the possibilities of person getting cancer based on certain attributes. The data is highly imbalanced. As per client requirement I have to report model performance based on any one of these 4 metrics AUC_Weighted normalized root mean square log loss Accuracy  Can you suggest me which one should I use? The equals() method in Java works unexpectedly on Long data type How to integrate $\frac{1}{\sqrt{1+x^2}}$ using substitution? How you integrate $\frac{1}{\sqrt{1+x^2}}$ using following substitution? $1+x^2=t$ $\Rightarrow$ $x=\sqrt{t-1} \Rightarrow dx = \frac{dt}{2\sqrt{t-1}}dt$... Now I'm stuck. I don't know how to proceed using substitution rule. How do I connect to a MSSQL database using Perl's DBI module in Windows? How do I connect to a MSSQL database using Perl's DBI module in Windows? nginx open reverse proxy? How bad for TeX is omitting braces {}, even if the result is the same? Sometimes writing braces and omitting them produces the same result:  \tilde{\psi}  \mathrm{e}^{\mathrm{i} \pi}   vs  \tilde \psi   \mathrm e^{\mathrm i \pi}   Or (taken from Werner's comment below)   \frac{1}{2} vs \frac12   If that's the case, how bad for the quality of my code is omitting them? Of course, if one compiles a pair of formulas, there is no difference. But, since I ignore how TeX works, my point is: if one writes long codes with these habits,   doesn't TeX go somehow crazy because I'm not writing as it expects?   For instance, does it have any effect on how fast are long documents compiled? Any reason to keep them? How to delete entry in Auto Complete in Microsoft Edge How do I delete an unwanted entry in AutoComplete in Microsoft Edge?  I have tried everything including highlighting with the down arrows and nothing works. How do I catch a PHP fatal (`E_ERROR`) error? I can use set_error_handler() to catch most PHP errors, but it doesn't work for fatal (E_ERROR) errors, such as calling a function that doesn't exist. Is there another way to catch these errors?  I am trying to call mail() for all errors and am running PHP 5.2.3. I'm running into this weird problem with Google spreadsheets: if the cells have comments on them and I sort the spreadsheet, the rows sort but the comments stay in the same position, and don't move with the cells they're attached to.  In other words, the cells look like this:  A C  &lt;-- comment on this cell B   and then I sort by this column:  A B  &lt;-- comment remains on this cell (stays in position) C  &lt;-- comment should have remained attached to this cell   This means that sorting is completely broken and I can't use it at all, because I clearly need the cell comments to stay with the cell they're attached to.  Is this a bad bug in Google Spreadsheets, or am I missing something here? After an AJAX request, sometimes my application may return an empty object, like:  var a = {};   How can I check whether that's the case? Is there a list of error codes for Minecraft? WinBUGS: Multiple definitions of a node So this question is about the BUGS modeling language. So you either know it or have no clue. I'm a newbie to this so it's been driving me mad. I want to define a simple two-state hidden Markov model (HMM) where the emission of each state follows a Normal distribution. I have an array data of Nxl dimension where each row is a subject and column is a continuous variable Time associated with the subject. So in WinBUGS, I would define the model as:   for(i in 1:N) { # for each subject     # Sample the initial observation     Time[i, 1] ~ dnorm(mu[State[1]], tau[State[1]])      for(j in 2:l[i]) { # for each observation         # Sample the observed variables         Time[i, j] ~ dnorm(mu[State[j]], tau[State[j]])         # Sample the hidden states         State[j] ~ dcat(P[State[j-1], ])     } }  # P is the transition matrix of the hidden Markov chain P[1, 1:2] ~ ddirch(Pinit) P[2, 1:2] ~ ddirch(Pinit)  # Set the initial states State[1] ~ dcat(Pinit)  # Sample the initial params mu[1] ~ dnorm(200, 1.0E-6) mu[2] ~ dnorm(400, 1.0E-6)  # The precision params tau[1] ~ dgamma(0.001, 0.001) tau[2] ~ dgamma(0.001, 0.001)   Initial values have also been provided via R2WinBUGS. The model is syntactically correct. But when I run, I got this error: "multiple definitions of node State[2]"  Can you please tell me why and how to solve this? I've searched around on the error but each has their own specific case and there's not a generic solution or explanation as to why this arises. Recovering accidentally deleted files I accidentally deleted a file from my laptop. I'm using Fedora. Is it possible to recover the file? Why should we typedef a struct so often in C? Settings disappeared in Ubuntu 19.10 I usually go to the right top corner and at the drop down menu I select the tool icon to go to the settings.  However, 19.10 does not have a tool icon.  How can I go to settings now? miktex-makepk - PK font HieroB could not be created I am depressed, after trying to install HieroTeX with MikTex 2.9 and TeXnicenter for four weeks without succeeding. I installed hieroglf, it works perfectly, but has only 60 signs. I followed the main advices, so I created a folder texmf-Local , throwed in  the content of HieroTex3.5 and Hiero-Type1.3.1.4 , put the axmf , mf and sty files where I think they belong, put that directory  texmf- local in the path searched by Miktex, updated map and file databases fo Miktex. Still the files can be compiled but Hiero fonts are not found.  Te main errors I can detect from log are the following:   " No file egypto.sty.tex found" and  "  "miktex-makepk - PK font HieroB could not be created." and similar for other fonts Thanks