According to Newton's third law, if I push an object the object should push me back with the same and opposite force. So there should be no net force, which means that it shouldn't be displaced (pushed).  But in reality it's not!!! How do I understand this?
Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?
Set the size of pgf picture? I have a pgf picture which I insert with:  \input{m1.pgf}   But the image is too big. Instead of regenerating a smaller image, I'd rather take advantage of vector graphics, and have XeLaTeX scale it. How do I set the width of pgf picture (keeping its aspect ratio)?  MWE  tex:  \documentclass{article}  \usepackage{fontspec} % enagles loading of OpenType fonts \usepackage{polyglossia} % support for languages  % fonts: \defaultfontfeatures{Scale=MatchLowercase,Mapping=tex-text} % without this XeLaTeX won't turn "--" into dashes \setmainfont{DejaVu Sans} \setsansfont{DejaVu Sans} \setmonofont{DejaVu Sans Mono}  % pgf: \usepackage{pgf}  \begin{document}  \input{m1.pgf}  \end{document}   Sample pgf:  (it's too big to cite it here, and I can't make much smaller). We always change subject and verb positions in whenever we want to ask a question such as "What is your name?". But when it comes to statements like the following, which form is correct?        I don't understand what are you talking about.   I don't understand what you are talking about.      Another example        Do you know what time is it?   Do you know what time it is?      Another example        Do you care how do I feel about this?   Do you care how I feel about this? Update: Failed to lock /var/cache/apt/archives/lock How can I unlock a password locked rar file without knowing the password? I have .rar file that is password protected, but I accidentally have forgotten the password. The file extremely important to me.  How can I get my file back? In windows, there was many programs that could remove the password of such a file. Is there one for Ubuntu? How do I include a custom class file in a module? In Drupal 7 module development, I could include a custom inc, api, or php class file using the  directive in the module.info file or the drupal_load_included() function.   With D8 using PSR, what is the proper way to package up a "plain ole PHP object" and reference it in DefaultController.php? Think something like: $a = new POPO();.  Is just giving the PHP file containing the class a namespace sufficient? How does the controller (or module in general) know to reference or scan for that class? Problem on Linear Diophantine Equation over 3 variables How to solve $ax+by+cz=d$ over integers where $a,b,c,d$ are integers? ls: cannot access .gvfs: Permission denied show all my unanswered questions from SE Any way how to get    my all un-answered questions  from across all SE sites? Good Number Theory books to start with? I'm in Grade 11. I'm interested in elementary number theory and would like properly study it. I'm not intending to enter any competitions. Is it possible to recover an email that has been clicked "delete forever" in the trash folder? Why can rm remove read-only files? Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice? Is an automorphism of the field of real numbers the identity map? Is an automorphism of the field of real numbers $\mathbb{R}$ the identity map? If yes, how can we prove it?  Remark An automorphism of $\mathbb{R}$ may not be continuous. I've heard a lot about the Undying Lands but I don't fully understand how they're different from Middle-earth and why only certain people/races are allowed to go there.  Can someone explain? I have a sight hosted on .ie domain but it is near the NI(Northern Ireland) border and the business has a lot of NI traffic. So when someone searches in NI with certain key words I would like the site to appear in the results, it currently doesn't.   I have seen this post    But was wondering the best way around this. Would it be to create a .co.uk version that redirects to the .ie site? Or would I have to create a separate .co.uk site?  Any help appreciated thanks. Example of a function $f$ on $X$ to $\mathbb{R}$ which is not $X$-measurable but $|f|$, and $f^2$ are measurable. Question  The following is from Bartle:  Give an example of a function $f$ on $X$ to $\mathbb{R}$  which is not $X-$measurable but is such that $|f|,$ and $f^2$ are measurable.  Relavant Information  A family $\textbf{X}$ of subsets of $X$ is a $\sigma$ algebra in case:   $\phi, \mathbb{R} \in \textbf{X}$ $X \setminus A \in \textbf{X}$ if $A \in \textbf{X}$ If $(A_n) \in \textbf{X}$, then the union $\bigcup_{n=1}^{\infty} A_n \in \textbf{X}$  Any set in $\textbf{X}$ is called $X-$ measurable.   A function is $X-$ measurable if for every real $\alpha$, the set $\{x \in X : f(x)&gt;\alpha\}$ belongs to $\textbf{X}$  Attempt  Consider the following function: $$f=\begin{cases} 1 &amp;\mbox{ if} \ x \not\in\mathbb{Q} \\                   -1 &amp;\mbox{ if} \ x \in \mathbb{Q}  \end{cases}$$ defined from $\mathbb{R}$ to $\mathbb{R}$ with $\textbf{X}$ being the Borel algebra (the $\sigma$ algebra generated by all open intervals $(a,b)$) Then if $\alpha \in [-1,1)$, the set $\{x: f(x)&gt;\alpha\}$ consists of the irrational numbers. If I can show that the irrationals are not in the Borel Algebra, then I would be done since $|f|=f^2$ is a constant and easily shown to be measurable. Unfortunately I do not know how to show that the irrationals are not in the Borel Algebra.  Edit it has been brought to my attention that the irrationals are in the Borel algebra. I think this is because the rationals, being countable, can be shown to be in the Borel algebra by constructing appropriate small neighborhoods around each rational and then taking the intersections. I now seek to construct a set that is not in the Borel algebra  Alternatively I have tried to define a set other than the irrationals that is not in the Borel Algebra and define a similar function but to no avail. I am currently self studying this book so it would be of great help to me if the answer could contain heuristics on how to tell when a set if borel measurable (although I do not require this in the answer). Why am I still getting a password prompt with ssh with public key authentication? Which are the spec bits in this cache? Tangent lines to ellipse from external point Does someone falling into a black hole see the end of the universe?