Inheritance tax for reputation
Shouldn't rep gains from old questions & answers eventually stop (or at-least reduce)?
Fantasy/scifi combo - band of travelers who must get from "sphere" or domain to domain - each geographic area is ruled by a magician - it turns out later these are people who are unwittingly tapping into the computer grid they all live on to alter their own reality? What purpose does downvoting questions serve? Normality of subgroups and Sylow groups under homomorphisms... Prove or disprove: if $f:G \rightarrow H$ is a surjective group homomorphism, then   1) $f(A)$ normal implies $A$ normal.  2) $S$ is a p-Sylow subgroup of $G$ implies $f(S)$ is a Sylow-p subgroup of $H$.   I believe 1 is false since I believe we need injectivity, but I cannot think of a counterexample...  I believe 2 is true but do not know how to show it... Suppose we have a natural number $n \ge 0$.  Given natural numbers $\alpha_1,\ldots,\alpha_k$ such that   $k\le n$ $\sum_i \alpha_i = n$   what is the maximum value that $\Pi_i \alpha_i$ can take?  I'm quite sure that there is a theorem telling me the result, but I cannot find it. For sure an upper bound is $n^k$ but I'm searching for a real upper bound. I'm pretty sure that upper the bound should be $n^2$, but I don't know I could prove it. I have just bought a Nikon 50mm f/1.8D prime lens.  I took this picture (leg of my glasses frame on a mouse, and a LED desk lamp is on top of it) : f1.8, 1/80s, ISO 200   The purple fringing is right in the middle of the picture. Does it happen very often to this lens? How to install PHP from source with latest cURL package on Linux? I simply have to use the latest cURL version (7.21.3) with PHP on my webserver. (Has to do with specific bug fixes)  It is not available by default on most current Linux variant repositories. (Natty Narwhal by Ubuntu is the only one and it's still in beta stages) - so I cannot simply run "aptitude install php5-curl" or similar to get it (the very latest version of cURL) installed.  How would one go about installing the very latest PHP + cURL packages?  Is it as simple as changing the to-download file for cURL in a repository somewhere? (ie. changing a text file's entry somewhere from  to  or something..?)  Basically I need the very latest cURL library running with PHP on Linux. How would you personally go about doing that? Backup of clients' directory to Windows Server 2008 what could cause a script to fail to find python when it has `#!/usr/bin/env python` in the first line? Trying to get casperjs running on Ubuntu 12.04. After installing it when I run I get:   09:20 $ ll /usr/local/bin/casperjs lrwxrwxrwx 1 root root 26 Nov  6 16:49 /usr/local/bin/casperjs -&gt; /opt/casperjs/bin/casperjs  09:20 $ /usr/bin/env python --version Python 2.7.3  09:20 $ cat /opt/casperjs/bin/casperjs | head -4  #!/usr/bin/env python  import os import sys  09:20 $ casperjs : No such file or directory  09: 22 $ python Python 2.7.3 (default, Sep 26 2013, 20:03:06)  [GCC 4.6.3] on linux2   So Python is present and runnable, casperjs is pointing to the right place and it is a python script. But when I run it I get "No such file".   I can fix it by changing the first line of the casperjs python file from:    #!/usr/bin/env python   to:   #!/usr/bin/python   Result:   $ casperjs --version 1.1.0-DEV   I managed to fix it, but I'm wondering why it didn't work with #!/usr/bin/env python, since that seems to be a normal interpreter line. Do I have something configured wrong?   Here are the steps to get casperjs:   $ git clone git://github.com/n1k0/casperjs.git $ cd casperjs $ ln -sf `pwd`/bin/casperjs /usr/local/bin/casperjs $ casperjs : No such file or directory How do I stop the excel file being in use? I'm opening an Excel file and I'm getting the File in use pop-up that says it's locked for editing by me. However, I've not got it open on this computer (I think I had it open and my machine blue-screened). How do I go about fixing this?  Should specify, this is a file on a file share.  edit I'm not talking about if this is being used by another user on another machine, this is only accessible by me on this file share. This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post. This problem is from assignment 5.  a) Prove that the relation $x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$. b) Describe the elements $a$ whose conjugacy class (= equivalence class) consists of the element $a$ alone.  a) Let $G$ be a group and $R$ be a relation on $G$ defined by $a\sim b$ if $a$ is conjugate to $b$.  Then $a\sim b$ if there is a $g\in G$ such that $a = gbg^{-1}$.  Let $a$ be an element of $G$.  Then $a=eae^{-1}$.  So $a\sim a$ and $R$ is reflexive.  Let $a$ and $b$ be elements of $G$ such that $a\sim b$.  Then there is a $g\in G$ such that $a=gbg^{-1}$.  Then $b=g^{-1}ag$.  Since $g^{-1}\in G$, $b\sim a$.  Hence, $R$ is symmetric.  Let $a,b$, and $c$ be elements of $G$ such that $a\sim b$ and $b\sim c$. Then there are elements $g,g^\prime\in G$ such that $a=gbg^{-1}$ and $b=g^\prime cg^{\prime -1}$.  Then $a=g(g^\prime c g^{\prime -1})g^{-1}=(gg^\prime)c(g^{\prime -1}g^{-1})=(gg^\prime)c(gg^\prime)^{-1}$. Since $gg^\prime\in G$, $a\sim c$.  Hence $R$ is transitive.  Therefore $R$ is an equivalence relation on $G$. b) Let $S$ be the set of elements of $G$ such that, for $s\in S$, $s=gsg^{-1}$ for any $g\in G$.  Then $sg=gs$.  So $S$ is the set of elements that commute with every element of $G$.  In other words, $S$ is the center of $G$. Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem. Thanks. What type of buildings offer what level of jobs? There are three tiers of workers (as is everything else); tier 1, 2 and 3. What I am having a hard time with is figuring out what I can build to target workers from each of the tiers. I gather what I am sure everyone else has, low tech industrial (regardless of density really) provides mostly tier 1 jobs.  But what are my other building options for tier 1 jobs? If I want to target tier 2 or 3 what types of buildings should I consider? GameJolt is a gaming platform/website that offers API access with features like achievements tracking for users, etc. I can use the API no problem on my tests but what I'm concerned about is the private key that is issued to my game. How do I ensure that it's protected from people that want to decompile my game? Once  they get the API private key, they will be able to do anything with it. How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto the cardioid $R=2(1+\cos \theta)$? I tried to create a Windows 10 USB boot medium with WoeUSB. I formatted a USB drive with an NTFS partition, but WoeUSB complains with:  Installation failed! Exit code: 256 Log: WoeUSB v@@WOEUSB_VERSION@@ ============================== Mounting source filesystem... Error: File "/media/woeusb_source_1543626298_6098/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed.  You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1543626298_6098"... You may now safely detach the target device   I've also tried to start WoeUSB via command line, did not work.  sudo woeusb --partition Win10_1809Oct_English_x64.iso /dev/sdb   My iso is located in:     home/sawyer/Downloads/Win10_1809Oct_English_x64.iso  Thanks in advance! I've been trying to get windows installed for three nights now, so any help towards that goal is greatly appreciated. Lubuntu Installer Giving Error after Partition creation "YOUR SYSTEM MAY OR MAY NOT BOOT " I was replacing my Ubuntu 18.04 with Lubuntu 20.04. I wanted to keep my /home partition same. After creating /root , swap and changing mount point for /home partition the installer gave a warning that /boot/efi partition is not created Lubuntu 20.04 needs /boot/efi partition to boot. Please create a FAT32 partition and mount it as /boot/efi and enable flag esp. Then I created the /boot/efi  partition but there was no esp flag(s). I had installed Ubuntu 18.04 alongside windows10. What should I do now? How to insert an item into an array at a specific index (JavaScript)? How to install software or upgrade from an old unsupported release? Find Max Value for each month for the last 3 months, properly How do electric currents make light? In an incandescent light bulb, electrons flow through wires to the bulb, where is passes through a filament, and the filament lights up.  Does this work because of several high energy electrons losing some of their energy to disturb the electromagnetic field, creating photons? The electrons just leave the filament afterward and are replaced by more high-energy electrons from the negative terminal. Or does it work differently?  As a secondary question, is there a type of light bulb that directly converts electron flow to photons? How to line up the pieces at the coast near the shipwreck? In The Witness, I was walking along the coast, and I came upon this:    Now, since I've learned      that mazes can be embedded in the environment,   I see the puzzle here, but I just can't get the pieces to line up well enough.  Standing on the couch and walking all around it doesn't seem to get me a       functional maze.   Where do I need to stand to activate the puzzle successfully?