I have seen Inception many times. Every time I come with a new conclusion. What I feel is that he is in dream right from the beginning, when he comes to meet syto. But, this is also confusing that he see's his children's face at the end but still at the end Totem is still spinning. Any one with the answer.?
Sorry for the vague title--I don't want the title to be a spoiler.  I've seen the movie three times, and the last two times I looked specifically for clues to this question, but found none.  The final scene in  shows       Cobb's top spinning, as he goes off to be reunited with his children.  The top continues to spin, then the movie ends, without telling us if the top topples--and therefore revealing whether he's in the "real world" or still in a dream. Do we know if he was in a dream at the end of the movie?   I'm assuming the answer is that we simply cannot know.  But did I miss anything?  Were there clues that I missed?
problem with using loop inside the tabular environment Better than premium Is there something higher (better) than the word premium, or does it mean the best? Also, is there something in between premium and deluxe?  Graphically: Does any word fit here? > Premium > Does any word fit here? > Deluxe How can I reset $PATH to its default value in Ubuntu? I accidentally unset all the directories of $PATH while trying to add a new one in ~/.bashrc. I opened a new terminal window as I was editing and now $PATH is empty. I'm worried if I boot from another drive to find the $PATH I won't be able to boot into this drive again.  Basically, what is the default result of echo $PATH? Question Staging SE Been a few blogs on , and I get the point. However, would a staging SE help solve some of these issues like community overlap. I understand , but how can someone not yet a part of a community know to do so. Some of the point of SO is that you often don't know what to ask exactly, and we help clear that up. So, I wonder, rather than &quot;playing hot potato&quot; would it be useful to have a site that's simply for temporarily holding questions and such.  It would be the alternative to migrating to another site where you dump all responsibility on that site. This area, all communities are responsible for. It would be a good place to ask a question if you don't know where to ask. The blog I linked talks about phrasing to a specific audience. For someone that doesn't know, the audience is better at selecting which questions are directed at them. As SE grows, the amount of communities will mean more overlap. Right now it may be reasonable to expect people to be able to predict the best community, but will it always be that way?  Some restrictions:  It would be accessible by all communities. The question could be edited, but not answered. The question could be exposed to more easily tracked/understood/etc. automated janitorial work.  Just a helpful thought. Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$ Minecraft Laucher has no Versions So this if the first time this has ever happened too me and I was wondering what it is. I just downloaded Minecraft and there is no area where i can change my version too 1.8.9/1.7.10 all i see when I do it is blank  Im just Wondering on how come even tho i hit the Repair button on the minecraft.msi download it dosnt fix it... If there is a way too fix this let me know cause my friend wants too play and I cant cause of this.. A certain physics problem I have been working on has turned into a math problem. Particularly, I want to find the solutions of some equation of the form   $$f(x)=ae^{bx}+cx+d = 0$$  where $a, b, c,$ and $d$ are constant, real numbers that come from the physics problem and $x$ will be a real number. I do not know how to find the solutions of an equation of this form. In the special case where $c=0$, the solution is simply  $$x = \frac{\ln(\frac{-d}{a})}{b}$$  but for other values of $c$, I am stumped. If there is no exact form for the roots, is there a relatively simple way to estimate the roots? Load jQuery from Stack's CDN if Google's CDN is blocked (or always) How to start Skype 4 with Ubuntu 12.10? I've installed Skype and it's running all OK but I want it to start automatically when I log with my user.  How can I do that? How to clear Chocolatey cache in the free version? Installation-file-cleaning is currently only available in  () and .  The package installation files can easily take gigabytes of storage space and to my knowledge they only increase in size as the user updates packages and installs new software, with only your hard drive capacity as the upper limit.   I don't know if Chocolatey stores cache in one central location — something is saved to ~\AppData\Local\Temp but the majority is located in the lib* folders in ~\ProgramData\chocolatey. Also the log files in the logs folder total to over 100 MB on my system. Is there any way to fully clear Chocolatey cache without manually deleting directories? How to force Wine into acting like 32-bit Windows on 64-bit Ubuntu? Yesterday I upgraded my Ubuntu 18.10 to Ubuntu 19.04, and after the restart, the trash icon and my Desktop files have disappeared from the UI. If I go to the Desktop folder from my personal folder, I can see the files, but my Desktop is empty.  How can I show my files in the Desktop again? What is the standard/recommended font to use in papers? I looked around but did not find that anyone has asked this before, but what are the fonts that are standard/recommended while writing academic reports/papers? How do you change the size of figures drawn with Matplotlib? How to check if a column exists in a SQL Server table? Is there more to an interface than having the correct methods So lets say I have this interface:  public interface IBox {    public void setSize(int size);    public int getSize();    public int getArea();   //...and so on }   And I have a class that implements it:  public class Rectangle implements IBox {    private int size;    //Methods here }   If I wanted to use the interface IBox, i can't actually create an instance of it, in the way:  public static void main(String args[]) {     Ibox myBox=new Ibox(); }   right? So I'd actually have to do this:  public static void main(String args[]) {     Rectangle myBox=new Rectangle(); }   If that's true, then the only purpose of interfaces is to make sure that the class which implements an interface has got the correct methods in it as described by an interface? Or is there any other use of interfaces? Let $R$ be a commutative ring and $A=\{1,a,a^2,\dots\}$ for some $a\in R$. Prove that $A^{-1}R$ is isomorphic to $R[T]/(aT-1)$.    I guess I'm meant to find a surjective homomorphism between $A^{-1}R$ and $R[T]$ and then use first isomorphism theorem. What homomorphism should I use? Are orbiting planets an  example of perpetual motion? How to get a vertical bar which is longer than \mid ? sometimes when writing mathematical expression with partial derivatives, one needs to write a vertical bar afterwards and write the value at the which the partial derivatives are being computed as subscripts. See for example the bottom post here:    However, the \mid symbol doesn't produce a tall bar that corresponds to the size of the partial derivatives term. Is there a way to have a taller bar?   PS: Some other posts here mention \middle| but this doesn't compile on my computer.  Thanks in advance.... Is it theoretically possible that every person in this village has a different jar of coins? A village has about $1$ million residents. Suppose each resident has a jar with $100$ coins in it.Two jars are considered to be “equivalent” if they have the same number of 10c, 20c, 50c, $\$$1 and $\$$2 coins in them. How many different (i.e. nonequivalent) jars of coins exist? Is it theoretically possible that every person in this village has a different jar of coins?  I understood that if we have $k_1$ 10 coins in the jar where $k_1$ is between $0$ and $100$ inclusive, then there are $100-k_1$ coins of other denominations in the jar. Likewise, we also have $k_2$ 20c coins in the jar where $k_2$ is between $0$ and $100$ inclusive, so the combined number of 50c, $\$$1, and $\$$2 coins in the jar is $100-k_1-k_2$. And we always have some $k_1, k_2, k_3, k_4, k_5$, let's say, so that the sum of those $k$'s is $100$.  I got stuck since I don't know how to 'compare' the number of coins in jars for different residents.