Understanding proper classes vs sets: why the set of all cardinal numbers cannot exist?
Cardinality of a set that consists of all existing cardinalities
If I have several classes with functions that I need but want to store separately for organisation, can I extend a class to have both?  i.e. class a extends b extends c  edit: I know how to extend classes one at a time, but I'm looking for a method to instantly extend a class using multiple base classes - AFAIK you can't do this in PHP but there should be ways around it without resorting to class c extends b, class b extends a After hitting 80% LTV, my mortgage lender refuses to remove PMI. Any recourse? Why can't I left click on my Macbook Pro? How can I create a brace spanning multiple lines on the right side of an itemized list? I have an itemized list:  \begin{itemize}     \item Lorem     \item Ipsum     \item Sit     \item Dolor     \item Amet \end{itemize}   I want to create an accolade on the right side of 'Lorem' and 'Ipsum', and add a bit of text at the point of the accolade. The level of this text should be between the first and the second line. How can I get this done? I know that this machine does not work, via thermodynamics. I am asking for an analysis in terms of mechanics and magnetism.  Anyway, so here is the machine:   (source: )    The magnet (the red ball) pull the ball up the ramp, and then it drops the ball through the hole, which then rolls down, and go ups the ramp again. Thermodynamics shows that this can not work.  From a mechanics and magnetism perspective, what happens when you do this, and why can't it happen?  I have a source saying that it would work if it were frictionless and we didn't try to extract energy from it (), so in a certain sense, it is very close to possible (they didn't provide a full analysis though.)  Another Image: Let's consider it case by case:  Case 1: Charged particle is at rest. It has an electric field around it. No problem. That is its property.  Case 2: Charged particle started moving (it's accelerating). We were told that it starts radiating EM radiation. Why? What happened to it? What made it do this?  Follow up question: Suppose a charged particle is placed in uniform electric field. It accelerates because of electric force it experiences. Then work done by the electric field should not be equal to change in its kinetic energy, right? It should be equal to change in K.E + energy it has radiated in the form of EM Waves. But then, why don't we take energy radiated into consideration when solving problems? (I'm tutoring grade 12 students. I never encountered a problem in which energy radiated is considered.) Setting Low Disk Space Alerts on Windows Server 2008 What is the alternative for Teamviewer? Is there any Ubuntu alternative for team-viewer software for Windows? I can't run this latex script Is there a way to ignore flow errors? I have an auto launched flow that I would like to just ignore the errors of if they occur. I currently have several fault connectors going to a dummy assignment. However I keep receiving error emails which is what I am trying to avoid. How do I eliminate the vertical realignment when using arrayrulecolor with cmidrule? I'm using consecutive \cmidrule commands in conjunction with \arrayrulecolor to alternately hide and unhide horizontal rules in a table.  However, when \arrayrulecolor is used with \cmidrule, some odd vertical spacing is introduced. I'd like to eliminate it.  (I'm using longtable, so a colorbox, minipage, or anything else tied to a page won't work.)  Below is an image that introduces the challenge. The first block shows a \toprule.  My goal is to create a shaded border around the table, so I've added a dummy column.  The second rule shows a \cmidrule that skips the first column.  The third block shows how I can use a \cmidrule to fill in the whitespace with a shorter \cmidrule.  Finally, I want to recolor this short \cmidrule to the background color and restore the color later.  Note the jagged vertical skipping in case 4 compared to case 3.  Why would \arrayrulecolor change vertical alignment?  How can I eliminate the jagged edges?    Here is the code:   \documentclass[11pt]{article}  \usepackage{longtable} \usepackage{booktabs} \usepackage{color} \usepackage{xcolor} \usepackage{colortbl}  \setlength{\aboverulesep}{0pt} \setlength{\belowrulesep}{0pt} \setlength{\extrarowheight}{0.25ex}  \newcolumntype{L}{&gt;{\columncolor[gray]{0.8}}l} \newcolumntype{C}{&gt;{\columncolor[gray]{0.8}}c} \newcolumntype{R}{&gt;{\columncolor[gray]{0.8}}r}  \begin{document}  \textsf{ \begin{longtable}{LLLLL}  &amp; \multicolumn{3}{@{}L}{\small {\tablename\ \thetable{}} - demonstration of odd vertical alignment with arrayrulecolor} &amp; \\%  &amp; \multicolumn{3}{@{}L}{\small {case 1: the line below is a toprule}} &amp; \\% \toprule  &amp; \multicolumn{3}{@{}L}{\small {case 2: the line below is a cmidrule that spans the middle 3 columns.  Note the whitespace!}} &amp; \\%  &amp; \multicolumn{3}{@{}L}{\small {The challenge: hide the widespace giving the appearance of a spacing around a longtable.}} &amp; \\% \cmidrule[\heavyrulewidth]{2-4}  &amp; \multicolumn{3}{@{}L}{\small {case 3: the line below is 3 cmidrules, 1 each for the first and last columns and 1 for the middle}} &amp; \\%  &amp; \multicolumn{3}{@{}L}{\small {note how the cmidrules align vertically ... perfect!}} &amp; \\% \cmidrule[\heavyrulewidth]{1-1}\cmidrule[\heavyrulewidth]{2-4}\cmidrule[\heavyrulewidth]{5-5}  &amp; \multicolumn{3}{@{}L}{\small {case 4: Now, lets try recoloring the first and last cmidrules}} &amp; \\%  &amp; \multicolumn{3}{@{}L}{\small {how do I eliminate the odd vertical alignments?}} &amp; \\% \arrayrulecolor[gray]{0.80}\cmidrule[\heavyrulewidth]{1-1}\arrayrulecolor[gray]{0.0}\cmidrule[\heavyrulewidth]{2-4}\arrayrulecolor[gray]{0.80}\cmidrule[\heavyrulewidth]{5-5}\arrayrulecolor[gray]{0.00} \endfirsthead  &amp;  Arizona State University &amp;  &amp; ASU &amp;\\   &amp;   Baylor University &amp;  &amp; BAYLOR &amp;\\   &amp;   Boston University &amp; 164988 &amp; BU &amp;\\   &amp;   Brown University &amp; 217156 &amp; BROWN &amp;\\   &amp;   California Institute of Technology &amp; 110404 &amp; CALTECH &amp;\\   &amp;   Carnegie Mellon University &amp; 211440 &amp; CMU &amp;\\   &amp;   Case Western Reserve University &amp; 201645 &amp; CASE &amp;\\   &amp;   Columbia University &amp; 190150 &amp; COLUMBIA &amp;\\   &amp;   Cornell University &amp; 190415 &amp; CORNELL &amp;\\      &amp; Yale University &amp; 130794 &amp; YALE &amp; % \label{tab:schools} \end{longtable} }  \end{document} Correctly typesetting a tilde How do I set the tilde (~) character correctly in LaTeX?  There’s a  on Stack Overflow, with a lot of answers. But dare I say it? They all suck:   \textasciitilde is too high, \texttildelow is too low. $\sim$ can be tweaked to look more or less acceptable: {\raise.17ex\hbox{$\scriptstyle\sim$}} – but even that is a hack and uses the wrong symbol.   The point is – the tilde character is definitely an existing glyph in any font I am tempted to use. How can I just access and typeset that character, please? Without resorting to some other, similar-looking glyph that first needs to be nudged into place using a cunning combination of font size and raised boxes?  There must be a possibility to access that glyph directly from the font definition.  To demonstrate, look at this screenshot which attempts simply to display a C++ destructor of a type T (~T):    Compare this with the symbol we get in the browser: ~ – that’s what I want. How to vote on friends / colleagues ' questions (or answers) How to troubleshoot booting to a black screen on VirtualBox I was using 13.04 as a guest OS on my VirtualBox 14.2.18. Host is Windows 8. After upgrade to 13.10 Ubuntu does not start. I can see a black screen and blinking cursor. I am pretty new to Ubuntu. I suspect a problem with graphics drivers. I can access tty and all files (/home) are there. Enabling tftpd  sudo launchctl load -F /System/Library/LaunchDaemons/tftp.plist   Start:  sudo launchctl start com.apple.tftpd   See logs syslog -w  com.apple.xpc.launchd[1] (com.apple.tftpd[30687]) &lt;Warning&gt;: Service exited with abnormal code: 1   Or with log stream --process tftp --level debug  Filtering the log data using "process BEGINSWITH[cd] "tftp"" Timestamp                       Thread     Type        Activity             PID    TTL 2020-01-21 12:35:44.903240+0200 0x5292a    Activity    0x6afa0              31479  0    tftpd: (libsystem_info.dylib) Retrieve User by Name 2020-01-21 12:35:44.903949+0200 0x5292a    Default     0x0                  31479  0    tftpd: recvfrom: Resource temporarily unavailable   I also tried to run tftpd directly without launchctl sudo /usr/libexec/tftpd -d -i /private/tftpboot/ with the same results.  Earlier I used this configuration and it worked fine. But after some changes (may be OS update) it became broken. Current MacOS version is 10.14.6 (18G2022)    How to fix tftpd?    Appendix. Configuration file /System/Library/LaunchDaemons/tftp.plist has default content:  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt; &lt;dict&gt;     &lt;key&gt;Disabled&lt;/key&gt;     &lt;true/&gt;     &lt;key&gt;Label&lt;/key&gt;     &lt;string&gt;com.apple.tftpd&lt;/string&gt;     &lt;key&gt;ProgramArguments&lt;/key&gt;     &lt;array&gt;         &lt;string&gt;/usr/libexec/tftpd&lt;/string&gt;         &lt;string&gt;-i&lt;/string&gt;         &lt;string&gt;/private/tftpboot&lt;/string&gt;     &lt;/array&gt;     &lt;key&gt;inetdCompatibility&lt;/key&gt;     &lt;dict&gt;         &lt;key&gt;Wait&lt;/key&gt;         &lt;true/&gt;     &lt;/dict&gt;     &lt;key&gt;InitGroups&lt;/key&gt;     &lt;true/&gt;     &lt;key&gt;Sockets&lt;/key&gt;     &lt;dict&gt;         &lt;key&gt;Listeners&lt;/key&gt;         &lt;dict&gt;             &lt;key&gt;SockServiceName&lt;/key&gt;             &lt;string&gt;tftp&lt;/string&gt;             &lt;key&gt;SockType&lt;/key&gt;             &lt;string&gt;dgram&lt;/string&gt;         &lt;/dict&gt;     &lt;/dict&gt; &lt;/dict&gt; &lt;/plist&gt;   Update1 It seems port is in use. Why? Who?  $ sudo lsof -i:69 COMMAND PID USER   FD   TYPE             DEVICE SIZE/OFF NODE NAME launchd   1 root   23u  IPv6 0x55f5dbd8d897c847      0t0  UDP *:tftp launchd   1 root   57u  IPv4 0x55f5dbd8d897e687      0t0  UDP *:tftp launchd   1 root   59u  IPv6 0x55f5dbd8d897c847      0t0  UDP *:tftp launchd   1 root   60u  IPv4 0x55f5dbd8d897e687      0t0  UDP *:tftp   launchd uses UDP port 69. Why?  $ ps -ef | grep tftp 501 94727 48073   0  4:16PM ttys007    0:00.00 grep --color=auto tftp I've created a series of DEM files using the  tool from LAStools; however since I don't have a licensed version they have black streaks running across them. Does anyone know a good method for removing these streaks? Invalid token 'while' in class, struct, or interface member declaration in very simple code I am not sure what the problem is but I keep receiving this error when I try to use a while statement in my code.     Invalid token 'while' in class,   struct, or interface member   declaration   I want to use a while loop to have something continuously update while a statement is true.  The rest of my code is rather long but whenever I type in the syntax:  while(a&lt;b) { //do whatever i want it to do here }   It gives me that compiler error right off the bat. Not quite sure what the problem is. I am doing this in a C# windows application under the Form1.cs file with all the other event handlers (for buttons and such).  Thanks!    I was unaware that loops had to be placed within a method (fairly new to c#), but I tried it and no errors were returned. Thanks for your help everybody!  Previously, I just had the loop within the main class of the program. Massive 404 attack with non existent URLs. How to prevent this? The problem is a whole load of 404 errors, as reported by Google Webmaster Tools, with pages and queries that have never been there. One of them is viewtopic.php, and I've also noticed a scary number of attempts to check if the site is a WordPress site (wp_admin) and for the cPanel login. I block TRACE already, and the server is equipped with some defense against scanning/hacking. However, this doesn't seem to stop. The referrer is, according to Google Webmaster, totally.me.  I have looked for a solution to stop this, because it isn't certainly good for the poor real actual users, let alone the SEO concerns.  I am using the Perishable Press mini black list (), a standard referrer blocker (for porn, herbal, casino sites), and even some software to protect the site (XSS blocking, SQL injection, etc). The server is using other measures as well, so one would assume that the site is safe (hopefully), but it isn't ending.  Does anybody else have the same problem, or am I the only one seeing this? Is it what I think, i.e., some sort of attack? Is there a way to fix it, or better, prevent this useless resource waste?  EDIT I've never used the question to thank for the answers, and hope this can be done. Thank you all for your insightful replies, which helped me to find my way out of this. I have followed everyone's suggestions and implemented the following:   a honeypot a script that listens to suspect urls in the 404 page and sends me an email with user agent/ip, while returning a standard 404 header a script that rewards legitimate users, in the same 404 custom page,  in case they end up clicking on one of those urls. In less than 24 hours I have been able to isolate some suspect IPs, all listed in Spamhaus. All the IPs logged so far belong to spam VPS hosting companies.   Thank you all again, I would have accepted all answers if I could. How can I join these two meshes in a proper way? I know I can Ctrl J to join them, but how can I do so without having overlapping faces? How to change 'et al' to italic font in citation call-outs, with 'agsm' bibliography style