The Windows (10) Installer directory is massive, over 25Gb for me.  Is there anything that can be tidied up here?  Also, what's it for?  Follow up  As removing it seems like a bad thing can I store it somewhere else?  It definitely doesn't need to be on the SSD.
Has anyone successfully deleted the Windows Installer files successfully before? They are taking up 35.1% of my total hard drive space.  Which ones are needed and which ones can be purged?  In order to see this folder, I had to unhide system files by going to Windows Explorer > Organize (dropdown) > Folder and Search Options > view tab > uncheck ==> Hide protected operating system files (Recommended).  I used WinDirStat program to get these percentages. To see the image in full size, open it in a new tab.  I was told by someone that you should not delete these files, but then I found a utility--Windows Installer CleanUp Utility (very old version) that deleted these.  But it doesn't run on Windows 7.  If anyone has a later version that they found works, please let me know the path.
MySQL string replace We're injecting records into a journey using a Salesforce data event.  I also want to advance the people in the journey based on updates that happen in Salesforce (e.g., as an Opportunity record advances through the sales process), but I can't figure out how to do that.  I've read all the documentation I can find, but there doesn't seem to be a Journey Builder widget that will wait to be prompted by an event in Salesforce before continuing someone on a journey.  At the moment, I'm completely stuck.    I'd greatly appreciate any advice or information on how I can make journeys event-driven in this way.  Thanks very much! When I visit a website it sometimes puts cookies on my browser. Usually cookies keep track of browsing info from that particular site. If I don't delete those cookies and browse other websites, will the cookies be able to know which site I am browsing? Also, can any website read browsing history which is saved by browsers? Can any website know about my browsing history by help of cookies, browsing histories saved by browsers, or by any scripting language e.g. javascript? GCD of the already GCD Icon missing when application is launched I've created an application launcher in /usr/share/applications that launches rdesktop. The file specifies an icon name and I've added the icons to:   /usr/share/icons/HighContrast/48x48/apps /usr/share/icons/HighContrast/22x22/apps /usr/share/icons/HighContrast/256x256/apps /usr/share/icons/HighContrast/32x32/apps /usr/share/icons/HighContrast/scalable/apps-extra /usr/share/icons/HighContrast/24x24/apps /usr/share/icons/HighContrast/16x16/apps /usr/share/icons/hicolor/scalable/apps /usr/share/icons/hicolor/128x128/apps /usr/share/icons/hicolor/16x16/apps   I then drug the launcher to the taskbar and the launcher with the correct logo is visible in the taskbar. However, when I start the task, a new icon is created in the taskbar, a square with a question mark in the center.  What icons do I need and where, so that the taskbar displays the correct icon for the application when it is launched?  The .desktop file contents:   [Desktop Entry] Version=1.0 Terminal=false Icon=mswindows Type=Application Categories=Network; Exec=rdesktop win7shared1 -g 1680x1000  Name=win7shared1 GenericName=rdesktop Comment=Open windows desktop  Keywords=Windows StartupNotify=false Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$ #1115 - Unknown character set: 'utf8mb4' When I Import Mysql from local server to web ser it is showng me error 1115 - Unknown character set: 'utf8mb4' in Creating wordpress wp_comment table CREATE TABLE IF NOT EXISTS  `wp_commentmeta` ( // // ) ENGINE = INNODB DEFAULT CHARSET = utf8mb4 AUTO_INCREMENT =1;  #1115 - Unknown character set: 'utf8mb4'  My mysql version is Version information: 4.0.4, latest stable version: 4.4.10 (local version)  Version information: 4.0.10.7, latest stable version: 4.4.10( server version)  Please help me to solve out the error Why can't we see the selected reasons when there are pending close votes for a question? When users vote to close a question, the original poster can't see the selected reason why until after the question is already closed.  If they could see this information, they might be able to edit the question to make it more acceptable and averting the need to close it.  For example, the owner of this  cannot see the reason why his question is being voted to close: The Center of $\operatorname{GL}(n,k)$ The given question:  Let $k$ be a ﬁeld and $n \in \mathbb{N}$. Show that the centre of $\operatorname{GL}(n, k)$ is $\lbrace\lambda I\mid λ ∈ k^∗\rbrace$.  I have spent a while trying to prove this and have succeeded if $ k \subseteq \mathbb{R}$. So I imagine there is a nicer way to go about this. I have seen people saying take matrices where every element except one is zero in proving similar results but such matrices are not in $\operatorname{GL}(n,k)$ as they are not invertible.  What I have done.  I have said let $B \in$ Center then $B$ commutes with everything in $\operatorname{GL}(n,k)$. So take a permutation matrix, $P$ which swaps rows $i,j$ $P \neq I$. From this you can deduce that $B^T = B$ and that $B_{ii} = B_{jj}$. We can use the fact that $B$ is symmetric to find an orthogonal diagonalisation of $B$ by the spectral theorem.  This gives $QBQ^T = D \rightarrow B=D$. And as $B_{ii} = B_{jj}$ we can say $B = k * I$.   But the spectral theorem requires $B$ to be a real matrix.   How do I prove this for a general $k$?. Does the proof of Bolzano-Weierstrass theorem require axiom of choice? When selecting the terms of subsequence from each bisections, I thought axiom of choice might be required. But I'm not so sure whether or not, so please tell me. [edited] I'm sorry for the lack of explanation. I want to prove this statement: Let $a_1, a_2, \ldots \in \mathbf{R}$, and $(a_n)_{n\in\mathbf{N}}$ is bounded, then $(a_n)$ has some convergent subsequence.  The proof is as follows. Since $(a_n)$ is bounded, for all $n\in\mathbf{N}$,   $a_n \in I = [b, c]$.  Now, let $I_0 = I$ and if $I_n = [b_n, c_n]$,  we define $d_n = (b_n+c_n)/2$ and  if infinite terms of $(a_n)$ is included in $[b_n, d_n]$(resp. $[d_n, c_n]$), we will define  $I_{n+1} = [b_n, d_n]$(resp. $[d_n, c_n]$).If both intervals contain infinite terms, let $I_{n+1}$ be $[d_n, c_n]$. For all $n\in \mathbf{N}$, infinite numbers of $m \in \mathbf{N}$ exist such that $a_m \in I_n$ suffices. We take the sequence of natural numbers $(n(k))_{k\in\mathbf{N}}$which suffices $n(0) &lt; n(1) &lt; \cdots &lt; n(k) &lt; \cdots$ following this procedure: Now we have already selected $a_{n(1)}, \ldots, a_{n(k)}$, there are infinite numbers of $m\in \mathbf{N}$ which suffices $n(k)&lt;m, a_m \in I_{k+1}$, so let's take the minimum m out of it. Applying this process recursively, we obtain a infinite convergent subsequence(?). I think intuitively, by only repeating this process we can't obtain countable infinite terms of subsequence because we have to repeat infinite times. n-dimensional vector space isomorphic to the n-th product of a field as abelian groups Let $V$ be a finite dimensional vector space (of dimension n) over a field $F$. I need to show that $V$ is isomorphic to $F^n$ as abelian groups. However, I don't really understand what does "isomorphic as abelian groups" mean, my (poor) attempt to solve this was:  Let $f:V\to F^n$, $f((v_1,v_2,\ldots,v_n)):=v_1+\ldots+v_n$, clearly $f$ is a group homomorphism, but it is not biyective since, for example, in the case where $dim(V)=2$ and $F=\mathbb{R}$ we have $f((2,-2))=0=f((3,-3))$, I've also tried it by defining $f$ to be the product of a vector's entries but obviously it didn't work so I'm stuck!   I think this should be an easy problem but since I don't quite understand it, it's giving me problems. Thank you for your help. Simple explanation to the induction from the slowly changing $\vec B$ of a solenoid in the region of $0$ magnetic field Auto increment filename I have a need to collect some duplicate files and want to avoid name collisions. The problem is that this collection of files might be added to by another execution of my script before the files are cleaned out and just want to continue to increment the number.  I decided on a simple until loop to increment the number like so.  until [[ ! -f ${PWD}/DUPES/${num}-$1 ]]; do num=$((num +1)) done mv --no-clobber $1 ${PWD}/DUPES/${num}-$1   I can't imagine ever exceeding 1k files in an extreme example, so my questions are...  Is this a terribly inefficient way to achieve this? Should I be parsing the existing files to get the highest leading number to start incrementing from there, or is this ok for the extreme example I put forth?  Or is there a better way all together? A set with n elements has 2^n subsets I don't understand why a set with n elements has 2^n subsets. How is this calculated? I realize that {123} has empty set - 1-2-3-1,2-1,3-2,3-1,2,3 but how is the formula derived? I occasionally update my kernel from this web site    I have been always downloading 3 deb files for installing  linux header all, linux image and linux headers. I noticed one more deb file recently for 64 bit kernel called Linux-image-extra.  I would like to know what does kernel file Linux-image-extra do and should I also install it? I know cell phone cameras are the lowest rung, but when reading reviews of phones, the reviewers always have sample shots that are much better than what I can manage.  What are some ways to take decent shots with a cell phone camera?  (I'm thinking of the higher end Android or iPhone cameras). What should i use for better performance, nine-patch or drawable xml resource? How can I play the same world between PS4 and Mobile? Examples of patterns that eventually fail Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of "proof". I receive responses like: "surely if Collatz is true up to $20×2^{58}$, then it must always be true?"; and "the sequence of number of edges on a complete graph starts $0,1,3,6,10$, so the next term must be 15 etc."  Granted, this second statement is less logically unsound than the first since it's not difficult to see the reason why the sequence must continue as such; nevertheless, the statement was made on a premise that boils down to "interesting patterns must always continue".  I try to counter this logic by creating a ridiculous argument like "the numbers $1,2,3,4,5$ are less than $100$, so surely all numbers are", but this usually fails to be convincing.  So, are there any examples of non-trivial patterns that appear to be true for a large number of small cases, but then fail for some larger case? A good answer to this question should:   be one which could be explained to the layman without having to subject them to a 24 lecture course of background material, and have as a minimal counterexample a case which cannot (feasibly) be checked without the use of a computer.   I believe conditions 1. and 2. make my question specific enough to have in some sense a "right" (or at least a "not wrong") answer; but I'd be happy to clarify if this is not the case. I suppose I'm expecting an answer to come from number theory, but can see that areas like graph theory, combinatorics more generally and set theory could potentially offer suitable answers. How can I calculate what the effect of an extension tube will be?