What is the proof that $\int e^{-x^2} \cdot dx$ is not elementry.
How can you prove that a function has no closed form integral?
Solving binomial theorem via induction Integer solutions for $x^2-y^3 = 23$. As the title stated, I am wondering the integers $x,y$ that satisfy the equation $x^2-y^3 = 23$. Breadboard Confusion I just received the following breadboard in a electronics starter pack I purchased.    I am a little confused in how I would go about prototyping on this board, all the tutorials I have read state that the breadboard should have a positive and negative  input on it. But it appears this one doesn't.  Could anyone help clear my confusion? Why is free will a widely discussed, established concept? Does this concept emerge from religious / spiritual doctrine? Why is there so much interest in this topic?  If a neural-network based AI machine with a certain high degree of complexity scores a perfect 100 every run in a turing test, have we not already refuted the idea of free will? In fact, let me extend this reasoning, if ANY machine scores a single point in a turing test (and not 100), have we not already disproved (or alternatively put in great doubt the existence of) free will? If we already created a machine that can master a certain degree of human interaction, have we not then demonstrated that human interaction is programmable? (given enough time for the creation of a complex or more appropriately elaborative neural system).   From the perspective of an external observer, such a machine would be qualitatively human although intrinsically quantitative behind a stream of 1's and 0's. It would exhibit a type of decision making indistinguishable from that of a human. Does this not reduce the type of decision making we understand to be "free will" to something quantitative, deterministic, materialist? Get last result in interactive Python shell How can I work with file uploads during a Webdriver test? This is a canonical question, intended to provide a comprehensive answer to many related questions  During the course of a Webdriver test, I want to upload files. However, this opens a native file picker, which Webdriver doesn't seem to support interacting with. How do I interact with it? Before I met her I had a poor opinion of her.   As person had a poor opinion before a particular time in past (before He met her) so I think there should be had had.   There are some more example like this:   Before I went to the university, I worked/had worked as a carpenter for 5 years. Before I opened the door, I put/had put the key in the lock. Before I opened the door, I looked/had looked carefully into the barn for snipers.   In all these sentence, for me, it should be perfect tense.  I asked that question on another platform where I was told that if sequence of past event is obvious and sentences uses "before"and "after", we often use past tense. Which means we should use past tense in all these sentences. But I have another sentence "The train had left before I reached the station." If I follow above mentioned rule there should be "left" instead of "had left". But I am damn sure this sentence is correct with "had left".   Am I correct?  Thank you How to reset the Xorg / xserver? Xserver keeps crashing on my general user account both in Unity 3D and 2D. It doesn't do it on the guest account.  That's why I want to reset / rollback everything xserver related, hoping this is going to fix it.  Most answers on this involve sudo dpkg-reconfigure xserver-xorg. However, this does nothing for me (generates no output) and I read in other forums, that it's deprecated.  So, what's the current way to reset all xserver / xorg options; what's the alternative to sudo dpkg-reconfigure xserver-xorg? X crashes during work, not before login or so. And the effect of a crash is, that I get thrown out of the session, not a freeze or machine crash. What are the differences between Linux and Windows .txt files (Unicode encoding) I am only using the 128 character set defined in the original ANSI standard.  But as a whole how are the files implmeneted differently.    I am not concerned with the display, i.e. if a tab is displayed with 6 or 8 characters but the actual internal representation in memory  One difference I've heard is the use of \r\n (Windows) vs. \n for line termination (Linux). Why is "letter" not plural in "two letter words"? What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$? I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form $$f(x) = Ae^{i (kx - \omega t)},$$ using complex exponentials? Number of solutions of an arithmetic function's equation Say, an equation is given below \begin{equation} 2\pi(x) - \pi(2x)=\omega(x) \end{equation}  where $x$ is a positive integer, $\pi(x)$ is the prime-counting function, and $\omega(x)$ is the number of distinct prime factors of $x$.  I would like to know if this equation holds for finitely many values of $x$ or infinitely many.  If one uses asymptotic formula (from number theory) it can be written that \begin{equation} \omega(x) \sim \ln x / \ln \ln(x) \end{equation} (from )  and  \begin{equation} \pi(x) \sim x/\ln(x), \end{equation} so the above equation can be rewritten (after simplification) as \begin{equation} 2x\ln(2)=\ln(x)\ln\ln(x)\ln(2x) +f(x) \end{equation}  where $f(x)$ is an error term.  If  I plot left side (which is linear, supposed to be a straight line) and right side(a curve),assuming $ f(x) $ is 100% accurate, then the equation implies(?!) that the right will intersect left side. Since line can intersect a curve ($ln  $ function) finite times, so there are finite intersection point. So, can I say that there are only finitely many values of $x$?  graph example-   here f(x) is assumed as x + sinx  without the f(x)- How do I access my Windows partition? I have Ubuntu 12.04 installed on my HP G62-453 TU Laptop. I cannot access the contents of my hard disk partition E. Modified files in a git branch are spilling over into another branch I am working on a git repository with a master branch and another topic branch. I have switched to topic branch and modified a file. Now, if I switched to master branch that same file is shown as modified.   For example:  git status in git-build branch:  # On branch git-build # Changes to be committed: #   (use "git reset HEAD &lt;file&gt;..." to unstage) # #       modified:   cvsup_current #   Switch to master branch  [root@redbull builder_scripts (git-build)]# git co master M       builder_scripts/cvsup_current Switched to branch "master"   git status in master branch  [root@redbull builder_scripts (master)]# git status # On branch master # Changes to be committed: #   (use "git reset HEAD &lt;file&gt;..." to unstage) # #       modified:   cvsup_current #   Why is that the file is shown as modified in master branch even though it was modified in git-build branch?   My understanding was that the branches are independent of each other and when I change from one branch to another the changes do not "spill over" from one branch to another. So I am obviously missing some thing here.   Anyone got a clue stick? In ZFC, a good way of ordering sets by cardinality is by leveraging the notion of an injection. We define: $$X \lesssim Y \leftrightarrow \mbox{ there exists an injection } X \rightarrow Y.$$  Alternatively, we can leverage the notion of a partial surjection, by which I mean a partial function that hits every point of its codomain at least once.  $$Y \succsim X \leftrightarrow \mbox{ there exists a partial surjection } Y \rightarrow X.$$  Now in ZFC, these approaches are equivalent, in the sense that $$X \lesssim Y \iff Y \succsim X.$$  But if we just consider ZF (that is, we drop choice) then the equivalence breaks down. However, we've still got the forward implication, because the converse of an injection is always a partial surjection.  A specific question. Define that two sets are weakly equipotent iff $X \succsim Y$ and $Y \succsim X$. Question: does weak equipotence imply genuine equipotence? I'm guessing "no."  A general question: In broad terms, how would the structure of the cardinal numbers in ZF be altered by adopting $\succsim$ rather than $\lesssim$ as the fundamental order relation, and taking equality of cardinal numbers to correspond to weak equipotence of sets? I'm guessing this would hide a lot of the (usually very complicated) structure of the cardinal numbers in ZF.  Remark. The order symbols can be written \lesssim and \succsim. Baking IK into FCurves I have an object containing multiple models with several IK.  One model has fcurves (euler rotation only) which gives motor to linked IK models.  What I need is bake/convert all IK animations into FCurves.  Is it possible? mbstring is missing for phpmyadmin in ubuntu 16.04 When I installed phpmyadmin in Ubuntu 16.04 LTS, it gives me an error mentioned below.     The mbstring extension is missing. Please check your PHP configuration   then I tried to install php-mbstring, it says mbstring is up to date, Can anyone help me to solve this? I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? I'm looking for a way to access raster layers in an Esri File-GeoDatabase without using ArcObjects or ArcPy, specifically I would like to access the raster layers with GDAL. I understand that the GDAL FileGDB and OpenFileGDB give access to vector datasets within File-GeoDatabases, and that ESRI's own FileGDB C++ API does not support raster access.   Is anyone out there aware of any open source solutions? I flagged a question, , as "low quality" but a moderator declined it. I thought that the post was a low quality one and would like to know why the moderator did not.  Hopefully shedding light on this matter will avail me of the knowledge to be a better flagger in future.  My logic was that mysql-fetch-row is not supposed to return an array of results. If it does than its name would be mysql-fetch-rows.  What's your take on the situation?