By virtue of the nature of the question, I can't give concrete evidence, since I don't record my screen, but over the past few days, I've tried to change a downvote or an upvote after an edit has appeared (I know that an edit appeared, because the content of the post obviously changed), but SO has no record of such an edit, so I can't change my vote.  Anyone know what's going on here/experienced similar issues?  The only thing I can think of is that there's some sort of threshold for what constitutes an edit that is significant enough to warrant a record, but that seems to be flawed.  Or perhaps, there's a significant amount of lag between an edit and its recording, but that doesn't appear to be true from my experience.    Apparently there's a five-minute grace period, in which edits are not logged, but it makes no sense to me that I can vote one way, you can change your answer, and if this occurs in a certain time period, then I cannot change my vote unless an additional edit has been made.    The other posts, while very similar to this one, seem to be more concerned with when you want to undo a down vote, but what if the opposite is true and there isn't an incentive for the OP to change their post (I'm concerned with both issues).  The quick fix is to edit the question and change your vote, which seems inappropriate.  There should be a non-hackish way to do this.
A little background:  I do not know what the specifics are, but I've noticed that a quick edit after a post will often times not result in an edit being posted. It's as if there was no edit. Edit: According to Bart this amount of time is five minutes.  The problem:  A user made a really bad post (said that ~ in C# wrt integers was used for deconstruction). I down-voted said post. Post quickly disappeared (I guess poster realized they screwed up and took back the post). Later, I come back and see my down vote but the answer is now correct (that ~ is the bitwise complement operator). I try to get rid of my down vote because it is no longer appropriate. However, it has been about half an hour and there is no edit posted (presumably the poster made an edit within the non-posting edit window) so I can't take my vote back.  Suggested solution:  If post gets edited (even within the non-post edit window) mark all the votes as changeable. I would guess that this would either involve an update on a table of votes or adding a column for last edit time which is not bypassed by the grace period. I realize that this may be an entirely non-trivial change, but unless the non-posting of edits is somehow changed to make sure the edit was trivial it seems this is necessary.
What are the possible catch bonuses and how much experience do they reward? Prove that all cyclic groups of the same order are isomorphic I want to prove that 2 cyclic groups of the same order are always isomorph. So, let $G,H$ be cyclic groups with $|G| = |H|$. Then: I suspect the isomorphism would be the one that maps a generator g to a generator h. Thus, consider this function:  $f: G \rightarrow H$ defined by $f(g^k) = h^k$. I already showed that this mapping is surjective and a homomorphism, but I get stuck at the injectivity part. Can someone give a hint (my attempts: I tried to deduce whether the kernel is $e_G$ and I also used the definition of injectivity but I got stuck in both approaches)? How do I draw text at an angle using python's PIL? Using Python I want to be able to draw text at different angles using PIL.  For example, imagine you were drawing the number around the face of a clock.  The number 3 would appear as expected whereas 12 would we drawn rotated counter-clockwise 90 degrees.  Therefore, I need to be able to draw many different strings at many different angles. How to prevent LaTeX from line-breaking a phrase? How can I prevent LaTeX from putting line-breaks into a phrase?  I could replace dashes with  and spaces with non-breaking spaces, but I'm looking for a more general solution in case I need other characters in such phrases. I just ran the following command in a directory with several files, some owned by root, some by a normal user. I got a strange message:  $ sudo chmod -rwx * chmod: example-file: new permissions are ----w----, not ---------   Why the heck does chmod refuse to clear all permissions, if a file had group write rights? What is the thought behind this behaviour?  And is there a way to force removing all permissions in one step, without having to execute sudo chmod g-w * afterwards? Is the Ratio of Associative Binary Operations to All Binary Operations on a Set of $n$ Elements Generally Small? I started thinking about the number of associative (binary) operations on a set with $n$ elements today.  Looking online I found  which indicates only $113$ of the possible $19,683$ operations on a three-element set satisfy association.  So, $50\%$ of binary operations on a two-element set satisfy association, and less than $0.6\%$ of all binary operations on a three element set satisfy association.  For an $n$-element set, where $n$ denotes a natural number, is the ratio $R_{n}=A_{n}/B_{n}$, of the number of associative binary operations $A_{n}$ to the number of all binary operations $B_{n}$, in general small?  I don't mean the following questions as equivalent, but since they seem more concretely answerable in principle, does   $$ \lim_{n \to +\infty} \frac{A_{n}}{B_{n}} = 0 ? $$       Also, is $F : n \to R_{n}$ a monotonically decreasing function?  Some Background of the Question: In his Linear Algebra Problem Book 1995 on p. 6 Paul Halmos writes "The commonly accepted attitudes toward the commutative law and the associative law are different.  Many real life operations fail to commute; the mathematical community has learned to live with that fact and even to enjoy it.  Violations of the associative law, on the other hand, are usually considered by specialists only."  For all I know, Halmos might only have written that to motivate the study of Linear Algebra and doesn't quite literally mean what he appears to say.  But, if he means what he appears to say, and if $F : n \to R_{n}$ is monotonically decreasing, or $R_{n}$ is generally small, I think there's something amiss with what Halmos says, since non-associative operations seem so common that one may as well enjoy them. Is there a known well ordering of the reals? So, from what I understand, the axiom of choice is equivalent to the claim that every set can be . A set is well ordered by a relation, $R$ , if every subset has a least element. My question is: Has anyone constructed a well ordering on the reals?  First, I was going to ask this question about the rationals, but then I realised that if you pick your favourite bijection between rationals and the integers, this determines a well ordering on the rationals through the natural well order on $\mathbb{Z}$ . So it's not the denseness of the reals that makes it hard to well order them. So is it just the size of $\mathbb{R}$ that makes it difficult to find a well order for it? Why should that be?  To reiterate:   Is there a known well order on the Reals? If there is, does a similar construction work for larger cardinalities? Is there a largest cardinality for which the construction works? Can I safely uninstall games purchased from Steam? Can I uninstall purchased games from my computer and then later download them through Steam without having to re-purchase if I'd like to?   I'm running short on space on my laptop, looking to free up some space and wanted to be sure that I can safely re-download anything at a later time similar to how you can with the Xbox Live marketplace. I run a large bulletin board and I get spammers every now and again. My moderation team does a good job filtering them out but every time I IP ban them they seem to come back (I'm pretty sure it's the same person on some occasions, as the post patterns are exactly the same as are the usernames) but I'm afraid to ban them by IP address every time.  If they are on a dynamic IP address, I could be banning innocent users later down the line when they try to get to my forum through SERPs, but if I ban only via static IPs I know that I'm only banning that one person.  So, is there a way to properly determine if an IP address is static or dynamic?  Thanks. How to specify password in ssh command From the terminal I type: ssh user@ip and then it prompts for a password.  Is there a way to specify the password in the ssh command itself? Why do people have darker skin in sunnier climates? Best methods to fix broken tracks I've made a couple of PCBs which need the odd few 10 mil tracks, but are mostly 20/30 mil. Unfortunately the etching process isn't fantastic and there are numerous breaks in the traces, most of them small.  I've managed to convince solder lumps to go over the top of the smaller gaps, and have used components legs to bridge some of the larger ones. The solder lumps don't feel particularly reliable though, and there are some gaps which are too small and awkward to get a piece of wire across but too big to be bridged with just the iron.  Are there any standard ways to reliably fix up broken traces?  Update: Thanks for the suggestions everyone!  I found and tried out a silver conductive pen. As a first time user I found it difficult to dispense, and obviously I didn't use enough of it or mix it properly because it didn't even end up being conductive.  It seems like the main problem was that I was trying to use pieces of wire which are too short. I found some small gauge tinned wire and used longer lengths, running it over significant lengths of good track on either side of the fault. That makes it much easier to position, and you can tack them down one end at a time. How do we solve (i.e. get the closed form of) $\int \sqrt{1 + t^2} dt$ ?   shows the closed form of it but not the steps in solving it.  I think I need some algebraic trick..   I thought of some hyperbolic functions and their derivatives and equalities:  If I make $ t = \sinh x$, then I can reduce the integral to  $$ \int \cosh ^2 x dx $$ though I'm not sure if this is valid. But from here, I cannot go on evaluating the integral... The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ is _____ I tried by taking the odd $n$ values as in that case, the integral I suppose was easier to calculate. So, denote $I_n=n\int_{0}^{1}e^{x^2}x^ndx$, then we have : $I_1=\frac{e-1}{2},\\I_3=\frac{3}{2},\\I_5=5(\frac{e}{2}-1),\\I_7=7(3-e)$ Then I tried calculating (random) values using calculator as integration was getting cumbersome. $I_{31}=2.488$, $I_{51}=2.57$. I do not see any kind of recurrence so that I can find a general term for odd $n$. I also tried the method given . The idea was that since integral doesn't depend on $n$ considering $I(n)=\int_{0}^{1}e^{x^2}x^ndx$, then $I'(n)=\int_{0}^{1}x^n\ln(x)e^{x^2}dx$, but this also doesn't lead me to any conclusion as well. I believe I couldn't get to a proper approach to tackle this question. Can someone please help with the idea that involves in solving these type of questions? This morning I upgraded my system to Windows 10 2004, the upgrade went smooth and was through Windows Update. I am using Hyper-V as my virtualization program for virtual machines and to provide extra layer of protection to the system through core isolation. After the upgrade, I noticed that a new Virtual Switch was created with the name &quot;vEthernet (Ethernet)&quot; where &quot;Ethernet&quot; within the parentheses is the name of my primary network adapter. Also noticed this behavior has a specific pattern of creating new vSwitches correspond to the adapters you have, e.g. if you created a new Virtual Switch and restarted the system, a new additional switch will appear with the name &quot;vEthernet (your-new-switch-name)&quot;. Tried to remove Hyper-V and reinstall it but no luck. I am aware of a similar  on SuperUser but has no answers on it. Any clues for the root of the problem? How do I check whether a file exists without exceptions? gpgkeys: key C927EBE00F1B0520 not found on keyserver Possible Duplicate:    I am using 10.04 LTS - Lucid Lynx. I shutdown the computer while a software update was running. Then after I restarted my computer and while the update manager was running, I got this error:  Could not download all repository indexes The repository may no longer be available or could not be contacted because of network problems. If available an older version of the failed index will be used. Otherwise the repository will be ignored. Check your network connection and ensure the repository address in the preferences is correct. GPG error: http://toolbelt.herokuapp.com ./ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY C927EBE00F1B0520 Failed to fetch  http://ppa.launchpad.net/rabbitvcs/ppa/ubuntu/dists/**DISTRIBUTION**/main/binary-i386/Packages.gz 404  Not Found   I went through the answers to  and I tried this $ sudo launchpad-getkeys  Please wait... launchpad-getkeys is running an update so it can detect the missing GPG keys Trying to import all the missing keys gpg: requesting key 0F1B0520 from hkp server keyserver.ubuntu.com gpgkeys: key C927EBE00F1B0520 not found on keyserver gpg: no valid OpenPGP data found. gpg: Total number processed: 0 launchpad-getkeys has finished importing all missing GPG keys.  Try running sudo apt-get update - you shouldn't see any key  errors anymore  But when I run sudo apt-get update again, it again shows that the key was not found on the keyserver. How to solve this problem? My Situation:   About $36k USD in graduate student loans.  There are 4 different federal loans in play, each with a fixed rate of 6.8%.   $12k w/ ~$1.2k in unpaid interest  $10k w/ ~$1k in unpaid interest  $8k w/ no unpaid interest (all principal) $6k w/ no unpaid interest (all principal)  All loans are in repayment. Some loans are subsidized, some are not. This no longer matters now that they're all in repayment though, right?     Is there a most cost efficient way to pay these loans off?  Should the interest be ignored for now on the ones that have $1k in unpaid interest for the time being, because payments to the other two loans will will go directly to principal (minus the monthly compounded interest of course)?  On the surface, I would assume that since they're all the same interest rate, it doesn't really matter, but I'm not sure how the accrued interest would factor in. I'm not interested in psychological wins like debt snowballing. I'm looking for the route that will have me paying the least. What is the Killing form of $\mathfrak{gl}_{m}$? Consider the Killing form of the Lie algebra $\mathfrak{gl}_{m}$. Then $\{e_{ij}\}$ is a basis for this Lie algebra where $e_{ij}$ is a matrix with 1 in the $i$th row, $j$th column and 0 everywhere else. Then every $A = (a_{ij}) \in \mathfrak{gl}_{m}$ can be written as $A = \sum_{i, j = 1}^{m}a_{ij}e_{ij}$. Since $[e_{ij}, e_{kl}] = \delta_{jk}e_{il}-\delta_{li}e_{kj}$, we have $ad(a)e_{ij} = \sum_{kl}(a_{ki}\delta_{lj} -a_{jl}\delta_{ki})e_{kl}$. From this we have $$ad(a)ad(b)e_{ij} = \sum_{k, r, s}(a_{rk}b_{ki}\delta_{sj} + a_{ks}b_{jk}\delta_{ri} - a_{ri}b_{jk}\delta_{sk} - a_{js}b_{ki}\delta_{rk})e_{rs}.$$ From this how can I see that the Killing form is $2m tr(ab) - 2tr(a)tr(b)$. I know that the Killing form is just the trace of the above centered equation, but I seem to be getting confused with all the indices. How do I detach a process from Terminal, entirely? I use Tilda (drop-down terminal) on Ubuntu as my "command central" - pretty much the way others might use GNOME Do, Quicksilver or Launchy.  However, I'm struggling with how to completely detach a process (e.g. Firefox) from the terminal it's been launched from - i.e. prevent that such a (non-)child process   is terminated when closing the originating terminal  "pollutes" the originating terminal via STDOUT/STDERR   For example, in order to start Vim in a "proper" terminal window, I have tried a simple script like the following:  exec gnome-terminal -e "vim $@" &amp;&gt; /dev/null &amp;   However, that still causes pollution (also, passing a file name doesn't seem to work).