Prove that $T$ is invertible if $(T\circ T)+T −2I_V = 0$
How do i prove invertibility of this linear transformation
Will some parents be offended when being asked, "Is it male or female?" If I ask the parent about a baby's gender, will it be impolite or not appropriate to say, "Is it male or female?"  Is there any subtle difference, in terms of politeness, among   "Is it a boy or girl?" "Is it he or she?" "is it male or female?" ColdFusion adding extra quotes when constructing database queries in strings I am coding in ColdFusion, but trying to stay in cfscript, so I have a function that allows me to pass in a query to run it with   &lt;cfquery blah >   #query# &lt;/cfquery>   Somehow though, when I construct my queries with sql = "SELECT * FROM a WHERE b='#c#'"  and pass it in, ColdFusion has replaced the single quotes with 2 single quotes.  so it becomes  WHERE b=''c'' in the final query.  I have tried creating the strings a lot of different ways, but I cannot get it to leave just one quote.  Even doing a string replace has no effect.   Any idea why this is happening?  It is ruining my hopes of living in cfscript for the duration of this project I'd like to delete a file from my Time Machine backups, but there seems to be no option to do so in the Big Sur version of Time Machine. I go to the Time Machine menu and select &quot;Enter Time Machine&quot;. Then I see the view with the stack of windows. I browse to a file and select it. Now I want to delete it so it doesn't exist and take up space in backups. There is no option to delete it - either the action menu in the toolbar, or the control-click context menu. How do I delete a file from Time Machine backups? There used to be a way to do this. (I'd take a screenshot, but the key shortcuts for screenshots don't work in Time Machine. Not sure if this is just a Big Sur thing or if that's always the case.) Update: I should mention I'm using APFS for my Time Machine volume. That seems to be relevant. Also, I contacted Apple support about deleting entire snapshots (slightly different goal than the one here in this question). They said you can't do it anymore. It seems like there's some bugs here, because I have a &quot;Move to Trash&quot; option if I control-click one of my backups. It seems to work initially but then the backup comes back.  I don't like losing this much control over my files. I may look for another backup solution. tikz trees: How to not draw a single edge Changing the size of the mouse pointer in Ubuntu MATE 18.04 does not work I have Ubuntu 18.04 with the gnome-desktop  and parallel the Ubuntu MATE desktop installed. While I can easily change the size of the mouse pointer (DMZ-White) in the Gnome3 desktop , this does not work on the MATE desktop. I use for this the dconf-editor.  Maybe someone knows a solution?  Thanks a lot. If $\Gamma$ is satisfiable then $\Gamma$ is consistent We say that $\Gamma$ is consistent if for no $\phi$, then both $\Gamma\vdash \neg\phi$ and $\Gamma\vdash\phi$. We say that $\Gamma$ is satisfiable if there is a structure $M$ s.t. $\models_M\gamma[s]$ for alle $\gamma\in\Gamma$.  I want to show that if $\Gamma$ is satisfiable, then $\Gamma$ is consistent.  I'm thinking we assume that $\Gamma$ is not consistent, and then show that $\Gamma$ is not satisfiable. So if $\Gamma$ is not consistent then both $\Gamma\vdash \neg\phi$ and $\Gamma\vdash\phi$ for some $\phi$. But by soundness theorem then $\Gamma\models\neg\phi$ and $\Gamma\models\phi$, meaning for structure $M$, we have $\models_M\neg\phi[s]$ (whereas $\not\models_M\phi[s]$) and $\models_M\phi[s]$. So would this mean that $\Gamma$ is not satisfiable? I'm a little confused, because wouldn't this instead be a contradiction? We are in the combat phase:   I declared my attackers  My opponent declared his blockers, stating which attackers he was blocking I cast an instant, which automatically kills his blocker. There is nothing blocking my attacker now   Now we're in the damage phase. I said that my attacker now does damage and  reduces my opponent's hit points. My opponent said that because my attacker was blocked no damage could be done. I pointed out that the blocker was destroyed before the damage phase, so therefore he wasn't blocking, but he wasn't having it. (My attacker does not have trample)  Is this covered by a specific section in the rules? how I can draw an skew cylinder (rotate around x axis) and fill it (in 3D tikz)? I'm trying to typeset a table that would have a header in the first row (I'm not looking for a different/better solution to adding a header, but for a fix to this solution. Thanks). I want to achieve this by having a multicolumn cell spanning all the columns of the first row. The problem is that if the text is too long, the column widths are uneven, with the last column accumulating excess width. I would expect all of the columns to be of approximately the same width (although I cannot find a decent source that would say they should), given the fact that all the text in the second row is of approximately the same width.  I find this behaviour quite puzzling and have no idea what the cause could be. I know I could perhaps remedy this by manually setting the column widths, but am curious as to how to fix this without doing that (I do not need or indeed want the columns to be of the same width, but roughly proportional to the length of their content), preferably but not necessarily by using the tabular environment only (some other conflict with the document class I am using).   What is it that I'm doing or assuming wrong? And why?  MWE:  \documentclass{article} \begin{document}  \begin{tabular}{ccccc} \multicolumn{5}{c}{This is a piece of text. The longer it is, the longer the last column.} \\  1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 \\ \hline \end{tabular}  \end{document}   Resulting table. Notice how the last column of the second row accumulates excess width. Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$? $$\begin{pmatrix}1&amp;1\\1&amp;0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&amp;F_n\\F_n&amp;F_{n-1}\end{pmatrix}$$  Somebody has any idea how to go about proving this result? I know a proof by mathematical induction, but that, in my opinion, will be a verification of this result only. I tried to find through the net, but in vain, if someone has some link or pointer to its proof, please provide, I'll appreciate that.  Thanks a lot! Uncheck checkboxes by changing particular checkbox state I have custom fields in contacts form named checkbox1__c, checkbox11__c, checkbox12__c, checkbox13__c.  When I check checkbox1__c then I want checkbox11__c,  checkbox12__c,  checkbox13__c to be unchecked.  When I unchecked checkbox1__c then I want checkbox11__c, checkbox12__c, checkbox13__c to be checked.  Is there any way to do this by using validation-rules? If not no way to this by validation-rules, then what is the best way to do this? I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? What if the hard disk is partitioned into more than 26 sections in Windows? first post between 12/26 and 1/1   Does that mean your very first post as a user should be made in those days?  Or that you should be the first user to post any post on a site starting 12/26?  Or something else?  The first option seems somewhat more likely but I'm not sure I'm parsing the description right. Keyboard layout isn't kept upon reboot I had a problem with the keyboard layout changing from PT (I'm Portuguese) to EN automatically with the last Ubuntu updates in Ubuntu 13.10. After Ubuntu 14.04 came out, I formatted my computer and installed the new version.  After that I haven't had any problems until the recent Ubuntu base update 2 or 3 days ago, when I started having the same problem again. I even removed the English keyboard from the Keyboard configurations, left only the Portuguese one, but still, every time I reboot my PC I get the keyboard configured for EN, despite Ubuntu displaying the contrary?  How can I remove this? I don't want to format the PC again and I'm getting really tired of this problem, since it looks like many Portuguese/Brasilian Ubuntu users are having the same problem. Where can I find web design projects? I am a recently graduated graphic designer. I would like to know if there are any worthwhile websites that I could present my portfolio and receive or look for job offers.  I have came across the following freelancewebsites by searching the web that seem to meet my criteria:       (the most famous website for people seeking for employers and employees)   I've also found two articles providing reviews on these types of sites:       I am new to the online freelance market. As a result, I don't have any clue which websites are mainstream for graphic designers and illustrators (which are my specialties). It's not immediately discernible to me which sites are the ones that are not a scam and are also good place for establishing myself.  I'm mainly looking for the resources that experienced designers are familiar with. I'm looking to narrow it down to the ones that have been used by those established in the industry. As a result I decided to consult the matter here and ask for input. In C# why can't a conditional operator implicitly cast to a nullable type Tweak showlabels/showkeys - wrap the label Can showlabels wrap the label in the margin? A very similar question is , but the solution of @DavidCarlisle does not solve the more general case. Consider the following MWE:  \documentclass{article} \begin{document} \begin{figure}[ht]   \centering   \rule{1cm}{1cm}   \caption{default}   \label{fig:a very very very long and detailed label} \end{figure} \end{document}   When adding the package showkeys the output is:    Similar problem occurs with the showlabels package (whether the hack of @DavidCarlisle is used or not):   So, is there a way to fix it? Seeking open raw LiDAR or laser scanner data? If $f^2$ is Riemann Integrable is $f$ always Riemann Integrable?