In many fields of physics and engineering, when we want to describe an infinitesimal, for example, the electric field, we could say $dE(x_i,y_i) = e^{jkr}...dx_0dy_0$   Since derivatives are not fractions, does it still make sense, in a mathematically rigorous way to talk about infinitesimals and would this be the correct notation of describing it? What would be the rigorous way of dealing with infinitesimals?  --Edit--  The history of this question went from "duplicate to an irrelevant question" but once reopened was closed for being "missing context" despite proper english, a clear yes or no question with already great answers (which would be impossible if the question was indecipherable). It seems like those with points have been abusing their powers an incorrectly closing questions that they simply don't like.
In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $dy = f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential). Then if we rearrange we get $dy/dx$ which could be seen as a ratio.   I wonder if the author says this because $dx$ is an independent variable, and $dy$ is a dependent variable, for $dy/dx$ to be a ratio both variables need to be independent.. maybe?
Key to get help about current function I wrote a simple backup script which back ups my stuff on a remote server, everything is working great but I'd like to have some sort of report like "backup successful or not".  this is my script   # backup CHECK date1=`date +"%d.%m.%y - %H.%M"` host=`hostname` twdate=`date +"%d.%m"` performtw=`ls -la|grep "tw"|grep "$twdate" &gt; tmp1.txt` echo $performtw if cat tmp1.txt|grep "tw" then echo backup successfull printf "tw backup success!" | mail -s "tw backup check $date1 repor$ rm tmp1.txt else echo backup failure printf "sitename backup failure!" | mail -s "site backup check $date1 repor$ rm tmp1.txt fi exit   But this isn't working really well and I ask you if there's some simpler and more powerful way to do it? Basically it just needs to check if file exists with the name starting xyz and was created at date xyz. Possible to draw an Item in a Grid with only 3 sides of a Frame? How to install Anaconda on Ubuntu? How to secure my laptop so that hacking by physical access is not possible? Why is it that they decided to make String immutable in Java and .NET (and some other languages)? Why didn't they make it mutable? apt-get autoremove wants to remove linux headers Today I ran apt-get autoremove to remove un-needed packages and it wants to remove linux-headers-3.2.0-37 and linux-headers-3.2.0-37-generic  Reading package lists... Done Building dependency tree        Reading state information... Done The following packages will be REMOVED: libglademm-2.4-1c2a linux-headers-3.2.0-37 linux-headers-3.2.0-37-generic ttf-umefont    ttf-unfonts-core 0 upgraded, 0 newly installed, 5 to remove and 0 not upgraded. After this operation, 67.6 MB disk space will be freed. Do you want to continue [Y/n]?    Is it safe to remove these? My installed kernel is a newer version than the headers that autoremove lists.  uname -r 3.2.0-38-generic According to preliminary estimates, the project should be completed by 2020 at a cost of about RUB 40 bn.    or      According to preliminary estimates, the project should be completed by 2020 at the cost of about RUB 40 bn.    Are both options okay, or is the first better?   We are introducing the sum to the reader, so logically it should be the first option. But there's a lot of google-hits for "at the cost of" too. Characterizing Dense Subgroups of the Reals What is the difference between Gödel's completeness and incompleteness theorems? I'm trying to write a basic program in C using gedit or sublime text (which I prefer), but no matter what I do when I try to compile or run, or even while writing, I have no option to use 'stdio.h' or any similar package. Even when I start typing #include &lt;st the only word completion sublime suggests is 'struct'.  I've read dozens of threads, but all managed to fix this by installing gcc, which I've tried to reinstall multiple times, with no luck.  This is the output from gcc -v:  Using built-in specs. COLLECT_GCC=gcc COLLECT_LTO_WRAPPER=/usr/lib/gcc/x86_64-linux-gnu/7/lto-wrapper OFFLOAD_TARGET_NAMES=nvptx-none OFFLOAD_TARGET_DEFAULT=1 Target: x86_64-linux-gnu Configured with: ../src/configure -v --with-pkgversion='Ubuntu 7.2.0-8ubuntu3' --with-bugurl=file:///usr/share/doc/gcc-7/README.Bugs --enable-languages=c,ada,c++,go,brig,d,fortran,objc,obj-c++ --prefix=/usr --with-gcc-major-version-only --program-suffix=-7 --program-prefix=x86_64-linux-gnu- --enable-shared --enable-linker-build-id --libexecdir=/usr/lib --without-included-gettext --enable-threads=posix --libdir=/usr/lib --enable-nls --with-sysroot=/ --enable-clocale=gnu --enable-libstdcxx-debug --enable-libstdcxx-time=yes --with-default-libstdcxx-abi=new --enable-gnu-unique-object --disable-vtable-verify --enable-libmpx --enable-plugin --enable-default-pie --with-system-zlib --with-target-system-zlib --enable-objc-gc=auto --enable-multiarch --disable-werror --with-arch-32=i686 --with-abi=m64 --with-multilib-list=m32,m64,mx32 --enable-multilib --with-tune=generic --enable-offload-targets=nvptx-none --without-cuda-driver --enable-checking=release --build=x86_64-linux-gnu --host=x86_64-linux-gnu --target=x86_64-linux-gnu Thread model: posix gcc version 7.2.0 (Ubuntu 7.2.0-8ubuntu3) `   This is the code:   #include &lt;stdio.h&gt;  int main(void) { printf("hello, world\n"); }   When I compile using gcc, I get nothing, no error at least. but when I try to run using just ./hello.c this is what I get. Can the program counter on Intel CPUs can be read directly (that is without 'tricks') in kernel mode or some other mode? ClassNotFoundException: org.eclipse.jetty.util.component.AbstractLifeCycle running inside jetty So light travels slower in glass (for example) than in a vacuum. What causes light to slow down? Or: How does it slow down? If light passes through the medium, is it not essentially traveling in the "vacuum" between the atoms? I am having trouble understanding the estimation of an AR process. In some textbooks, the AR(1) process is defined as follows: $y_{t}=\theta y_{t-1}+ϵ_t$ (which does not contain a constant). So the OLS estimator is biased. I am confused about the cause of the bias. It is explained that $y_{t-1}$ is dependent on $ϵ_{t-1}$ although it is independent of $ϵ_t$. However in linear regression, if the equation does not contain a constant, we cannot make sure the expectation of disturbance is zero. So the OLS estimator is bias without a constant. Does it mean that the OLS estimator is unbiased if I add a constant in AR process? Javascript Date: next month I've been using Javascript's Date for a project, but noticed today that my code that previously worked is no longer working correctly. Instead of producing Feb as expected, the code below produces March.   My code looks something like this:   current = new Date(); current.setMonth(current.getMonth()+1); //If today is Jan, expect it to be Feb now   This code worked everyday up until today. Is this a Javascript bug or am I going about this the wrong way? With biblatex, is it possible to replace one author of an author list by a bibnamedash or idem string? With biblatex, the author can be replaced by a dash (or “idem”) in the bibliography. Is it possible to have this replacement also if there are multiple authors, and the first of these multiple authors is the same as the author of the book listed before? (It is somewhat difficult to describe, see the attached example instead, where “Buchautor, Hans-Wilhelm” should be replaced in book3 as well.)   I assume that it should be possible by customising \DeclareNameFormat, but I don’t know how.  Minimal example:  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{csquotes} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOK{book1,   author = {Buchautor, Hans-Wilhelm},   title = {Irgendein Buch},   location = {Buch am Wald},   date = {2000} } @BOOK{book2,   author = {Buchautor, Hans-Wilhelm},   title = {Ein anderes Buch},   location = {Berlin},   date = {2001} } @BOOK{book3,   author = {Buchautor, Hans-Wilhelm and Zweitautor, Zoran},   title = {Noch ein Buch},   location = {London and New York},   date = {2010} } \end{filecontents}  \usepackage[ style=authortitle, backend=bibtex8 ]{biblatex} \bibliography{\jobname}  \renewcommand*{\bibnamedash}{%   \bibstring[\mkbibbold]{idem\thefield{gender}}}  \begin{document} \nocite{*}  \printbibliography \end{document}   Edit 15/02/2011 17:14   I should have added that there was a feature request for biber which pointed back to biblatex. See .  Edit 21/06/2011 9:26  Is this somehow possible now with biblatex 1.4/1.5? I played a bit with uniquename/uniquelist, but I could not get it to work. Calculate first difference by group in R As we all know, going near a black hole (Gargantua in this case) slows down time, according to the theory of relativity.  So when Cooper comes out of the black hole, after spending a fair bit of time there, shouldn't he be much older than Brand who hasn't gone inside Gargantua? $f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki