I was wondering if there exists a pair of natural numbers $n, m \in \mathbb{N}$, such that $e^n = m$? Of course excluding the simple solution (0,1). Intuitively, I would say no. However, I am far from finding an argument, nor knowing which theory even treats these types of questions. Cheers
May $y=e^x$ be satisfied with both $x$ and $y$ be positive integers?  I think it is not possible as $e$ ,a transcendental number, when multiplied by itself would never result in rational number.  Am I right?
this works in viewport but not in render.  import bpy from math import *  def frame_handler(scene):     z = scene.objects['Lift'].location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_pre.append(frame_handler)   How to get it working in render? I've read  and changed from "bpy.data.objects" to "scene.objects" as already seen in the script. What am I missing? Blender v. 2.81.16  Edit. Tried that depsgraph thing mentioned in comments and changed to frame_change_post:  import bpy from bpy.app.handlers import persistent from math import *  @persistent  # maybe not relevant but doesn't harm anything? def frame_handler(scene, depsgraph):     z = scene.objects['Lift'].evaluated_get(depsgraph).location[2]     scene.objects['Text'].data.body = str(floor(z / 4.0) - 2)  bpy.app.handlers.frame_change_pre.clear() bpy.app.handlers.frame_change_post.clear() bpy.app.handlers.frame_change_post.append(frame_handler)   Now the Text doesn't show up at all in rendered (but works in viewport). Can you provide a list of objects that needs to be disposed in SharePoint? Electric charge is lorentz invariant I know that electric charge is lorentz invariant quantity and I can easily think of experiment to check that. Is a though experiment that can prove that also? Killing form on $\mathfrak{sp}(2n)$ I have the same question as  from a long time ago. Is there an easy way to see that the Killing form on $\mathfrak{sp}(2n)$ is $\kappa(x,y) = (4n+2) \mathrm{tr}(xy)$?  For example, the Killing form for $\mathfrak{sl}(n)$ can be found from the easier to calculate case of $\mathfrak{gl}(n)$ using the decomposition $$\mathfrak{gl}(n) = \mathfrak{sl}(n) \oplus \mathbb{C}.$$ I don't know a similar argument for $\mathfrak{sp}(2n)$ though. Scenario:   Create SymLink: C:\Data\workspaces --&gt; C:\Users\****\Documents\workspaces Navigate to C:\Data\Workspaces in explorer Click and drag the the path from the address bar onto "Quick Access" in the navigation pane.   Expected Result:   Clicking on the shortcut takes you to C:\Data\workspaces   Actual Result:   Clicking on the shortcut takes you to C:\Users\****\Documents\workspaces   How do you make it so that the shortcut points to the correct path. (the SymLink)  Command Used to create the SymLink:  mklink /D C:\Data\workspaces C:\Users\****\Documents\workspaces   Updated with pictures:  Please note the workspaces symlink inside C:\Data:    When I double-click on the symlink it works correctly. (note the address bar.    When i pin it to the Quick access bar, however, it uses the address that the symlink points to and NOT the symlink address. Exploiting JavaScript's eval() method How to get a toddler to start chewing and eating solids? My son is 18 months old and still doesn't want to chew and eat solid foods. We have to blend soups and other food into purée for him to accept it. If there is even a slight solid, he will automatically push it out of his mouth with his tongue.  I have had a breakthrough with breakfast where I don't blend as much and leave it a little chunky. He ate it but still pushed chunks of soft banana that were bigger out.  Some of my friends have kids that are 4-5 months younger, who are eating chicken cutlets.  Any ideas or proven methods for getting a child to start eating solids? How to find manually installed packages? I installed a plain Ubuntu 10.10 on my computer and installed some software via apt-get. Last week I managed to break everything and just started from scratch, and I need to reinstall my software. Is there some way to create a list with all the packages that I have installed manually?  So that it would give me a list like texlive, ... and not texlive, texlive-dep1, textlive-dep2, ... and all the standard packages removed?  If I could somehow figure out which programs out of the regular install I have removed, that would be awesome too!    Update 2015-05-23: I now use Ansible as configuration management on my systems. There I specify the packages to install. This serves the goal, installing all the programs on a fresh system, even better. So this question might be the entry into some light configuration management. Making images from single.php pointing to an attachment .php template Why does Quantum Field Theory use usually Lagrangians rather than Hamiltonains?  I heard many reasons, but I'm not sure which is true.   Some say it's just a matter of beauty, so Lagrangians are more beautiful because they don't break/separate the space-time variables (so space-time is a single variable, like in the Klein-Gordon Lagrangian and Hamiltonian).  Some say that Hamiltonians are not always Lorentz invariant.  Could someone explain in a little bit more details? I'm looking for ways to speed up the combat in my D&amp;D 3.5 game. It seems that turns - both player and non-player - simply take too long. I have thought about giving everyone a 30 second timer, but I'm afraid that might inhibit their ability to come up with strategy and tactics. How do I add a .sty file to my MacTeX/TeXShop installation? I've searched online, but I have not found any clear instructions how to permanently add .sty files to my TeXShop installation. I'm using a Mac with OSX (TeXShop is a mac only program).  What is the best way of doing this? The one comprehensive set of instructions I found .   I've got as far as extracting the files (running LaTeX on the .ins and . dtx files) but after that I don't know what to do. I also don't understand how to update the index of my distribution, and whether there are particular OSX specifics (the instructions are for Windows). How can native English speakers read an unknown word correctly? Show that $a_n=\sin(n)$ does not converge     My idea:  Take two subsequences: $a_{n_k}=\sin(\frac {\pi k} 2)$ , $a_{n_l}=\sin(\frac {2\pi l} 3)$  So: $\forall n$ : $\lim_{n\to\infty} a_{n_k}=1$, $\lim_{n\to\infty} a_{n_l}=-1$  So two inifinite subsequence converge to different limits thus the sequence $a_n$ doesn't converge.   Is that correct ?  Edit:   The contrapositive of the defintion of a limit of a sequence:   $\exists\epsilon&gt;0 : \forall n\in N : \exists n&gt;N \Rightarrow |x_n-L|&gt;\epsilon$  Take $\epsilon =1$ and we know that $\sin(n)$ is bounded so lets take it's supermum: 1  $|1-1|&gt;\epsilon=1\Rightarrow 0&gt;1 \Rightarrow$ Contradiction. Error on \usepackage {geometry} text property Is there a way to spellcheck the word under the cursor with a keyboard shortcut? Updating the repository isn't working When I run sudo apt-get update get this output:   sudo apt-get update E: Type '&lt;!DOCTYPE' is not known on line 1 in source list /etc/apt/sources.list.d/playonlinux.list E: The list of sources could not be read.   Also Ubuntu software Center is not opening. If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected? Possible Duplicate:          As the topic,if $A\subset\mathbb{R^2}$ is countable, does $\mathbb{R^2}\setminus A$ path connected??? I know the answer is it is path connected but not sure how to prove it. We have more than one content management system (eCommerce) running on our site and we want to know would it be wise to separate these systems and run on their own server for better performance, easier to manage and better for security, but our concern is the SEO impact.  Is it better to run site.com/this-is-our-other-platform/ or this-is-our-other-platform.site.com? Load R package from character string