I know that to show this I have to show there’s an injection from the $\varnothing$ to $\{\varnothing\}$. But how can one even define a function on the $\varnothing$?
I meet with term 'empty function' from time to time. It's high time to understand its nature. What is field( set of arguments) and what is image? ( set of value)?
How to stop people from using my domain to send spam? I receive Mailer Daemon messages saying certain emails fail. My domain is itaccess.org which is administered by Google apps. Is there any way I can identify who is sending emails from my domain, and how they are doing it without me creating an account for them?  Delivered-To: 7e949ba@itaccess.org Received: by 10.142.152.34 with SMTP id z34csp12042wfd;         Wed, 8 Aug 2012 07:12:46 -0700 (PDT) Received: by 10.152.112.34 with SMTP id in2mr18229790lab.6.1344435165782;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Return-Path: &lt;whao@www20.aname.net&gt; Received: from smtp-gw.fsdata.se (smtp-gw.fsdata.se. [195.35.82.145])         by mx.google.com with ESMTP id b9si24888989lbg.77.2012.08.08.07.12.44;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Received-SPF: neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) client-ip=195.35.82.145; Authentication-Results: mx.google.com; spf=neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) smtp.mail=whao@www20.aname.net Received: from www20.aname.net (www20.aname.net [89.221.250.20])     by smtp-gw.fsdata.se (8.14.3/8.13.8) with ESMTP id q78EChia020085     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:43 +0200 Received: from www20.aname.net (localhost [127.0.0.1])     by www20.aname.net (8.14.3/8.14.3) with ESMTP id q78ECgQ1013882     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:42 +0200 Received: (from whao@localhost)     by www20.aname.net (8.14.3/8.12.0/Submit) id q78ECgKn013879;     Wed, 8 Aug 2012 16:12:42 +0200 Date: Wed, 8 Aug 2012 16:12:42 +0200 Message-Id: &lt;201208081412.q78ECgKn013879@www20.aname.net&gt; To: 7E949BA@itaccess.org References: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; In-Reply-To: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; X-Loop: whao@whao.se From: MAILER-DAEMON@whao.se Subject: whao.se:  kontot avstängt - account closed X-FS-SpamAssassinScore: 1.8 X-FS-SpamAssassinRules: ALL_TRUSTED,DCC_CHECK,FRT_CONTACT,SUBJECT_NEEDS_ENCODING      Detta är ett automatiskt svar från F S Data - http://www.fsdata.se      Kontot för domänen whao.se är tillsvidare avstängt.     För mer information, kontakta info@fsdata.se      Mvh,     /F S Data      -----    This is an automatic reply from F S Data - http://www.fsdata.se    The domain account "whao.se" is closed.   For further information, please contact info@fsdata.se    Best regards,   /F S Data Send email with an attachment located in Google Drive I want to send a PDF attachment located on Google Drive from a Sheet.   Code I'm using is:  function sendEmails() {   var sheet = SpreadsheetApp.getActiveSheet();   var startRow = 2;  // First row of data to process   var numRows = 8;   // Number of rows to process   // Fetch the range of cells A2:B3   var dataRange = sheet.getRange(startRow, 1, numRows, 2)   // Fetch values for each row in the Range.   var file = DriveApp.getFilesByName('ScriptCarPass.pdf')   var data = dataRange.getValues();   for (i in data) {      var row = data[i];     var emailAddress = row[0];  // First column     var message = row[1];       // Second column     var subject = "Sending emails from a Spreadsheet";     MailApp.sendEmail(emailAddress, subject, message, {attachments: file});   } }   Everything works fine except the attachment - i.e. if I run without the attachment it works fine.  I keep getting error Invalid argument: inlineImages  I've also tried with:   attachments: [file.getAs(MimeType.PDF)]   but that gives error that .getAs isn't recognised. Showing that $\mathbb{R}$ is connected So I know that $\mathbb{R}$ is both open and closed. But given a set, $X\subset \mathbb{R}$, $X\ne \emptyset $ that is both open and closed, how does one show that $X=\mathbb{R}$?    Here is my attempt: Using the definitions I was given, $X$ open implies that for every $x\in X$ there is a $\delta \gt 0$, $(x-\delta,~ x+\delta)\subset X$.    Also, since $X$ is closed , $B=\mathbb{R}$\  $X$ is open.    However, I don't know how to proceed. NB: This is not a homework problem. How do I deal with NAs in residuals in a regression in R? Lewis Carroll's Pillow Problem via Bayes' Theorem In Pillow Problems and a Tangled Tale Lewis Carroll presents the following problem:     A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter?   One can easily reason that in the end, the bag must be in one of three states:   Black remains, new white taken New white remains, original white taken Original white remains, new white taken   In two of those states, a white counter remains to be drawn. Therefore, the chance is 2/3.  How can one arrive to this answer using Bayes' theorem? Hide back faces in 3D View? How do you hide back faces so that you only see faces when its normal is facing the camera? When exporting it for use in a game, the face is rendered in only the direction of its normal, so this would be useful to have something similar. I have an org with hundreds of apex classes, all of which have api versions ranging between 30-37. Is there an easy way to bring them all to the latest api version at once without resorting to manual updates? Why does replication require primers while transcription does not? Prove that in any GCD domain every irreducible element is prime Even though a question may be closed by receiving 5 close votes, the votes do not necessarily need to agree.  I think this is a good behavior, but  (which it was) and found the question was closed as "not a real question".  This is unfortunate, while I'm happy to display my username and acknowledge that I voted to close, I'd like some additional transparency.  That is, if it was a 4-1 vote for "not a real question" vs "exact duplicate" I'd be interested in seeing that level of information.  The point is to be transparent about why the question was closed, and though 5 users may agree the question needs to be closed they may not agree why.  It's important to recognize all the reasons for closure, not just the majority reason.  I'd suggest displaying this information as something like:     closed on Jun 21 at 4:26 as:         not a real question by foo, bar, baz   exact duplicate by alice, bob      Once a question has been closed I'd argue it's more important to understand the rationale than it is to worry about an extra 2 lines of text. If the votes are 2,1,1,1 perhaps keep just 2 bullets, the first showing the majority vote, the second saying "for other reasons" as a summary of the change.  The point is to aggregate the summary by reason. Does the series $\sum_{n=1}^{\infty}|x|^\sqrt n$ converge pointwise? If it then what would be the sum? Are all oscillatory motions periodic motions? For example, if a pendulum system in the real world oscillates its amplitude and period will eventually decrease. Does that still count as a periodic motion? Since the motion doesn't have the same amplitude at equal time periods. EDIT:  It seems that I've also had edits that stacked well, so I'm not sure if I had a timing problem, or was just delusional.  The one thing that can be fixed, that I'll turn this question into, is a feature request so that when I go to re-edit (either within the 5-minute grace period, or before a suggested edit is approved), it brings up the old edit summary text.  Right now, it brings up a blank edit summary, and this replaced the first one I did.  This isn't really intuitive, and even knowing that's what it's doing, I still forget to put everything in.  Original Question:  It has happened a few times now, when on a site where I don't have edit privileges, that I make an edit.  I then see that the edit didn't work quite right, so I go back in to re-edit it.  This creates a brand new edit review, with an additional useless summary. How about we have the same grace period to re-edit your up-for-review edit, as there is for a normal edit? Of course, it wouldn't be possible once it's been approved. Yesterday, my laptop caught a virus which caused massive damage. Since them, I have been trying to recover important files before reformatting my computer, a task the virus has not made easy.   Restoration points predating the attack have been deleted.  Most of my folders show empty.  My Start menu is essentially empty, with the exception of Trillian and Mirror's Edge. The same goes for my Desktop, which only has programs which were installed after the attack.  Searching for files through my computer is pretty much useless, as it only rarely brings up anything. I suspect most of my files have not been deleted. While my folders show empty, uTorrent still does display them and I can open them from here. Unfortunately, when I select Open Containing Folder, the folder still shows as completely empty even if I'm currently watching a video from that very folder. Further adding evidence to the not-deleted-just-missing theory, the data recovery software I'm using (Restoration) cannot find only find an handful of the missing files.   If they were deleted, I could do a forensic recovery to get them back but since they're probably still somewhere on my computer, just out out of my reach, I can't find them.   Under those circumstances, is there a way I can recover those files? Output to stdout and at the same time grep into a file how to create facebook event in an android app? Return multiple values to a method caller How to say that the phone is held between shoulder and ear? What are common phrases an English native speaker would use for the pose of speaking on the phone where you use your shoulder to keep the receiver against your ear (and mouth), so your hands are free?  I have some ideas, but they all sound wooden, and I don't think I've ever heard anyone describe this pose in words. It's also pretty much impossible to google for a pose or look it up on leo.org or other dictionaries.  OK, since people keep asking for what phrasings I found, I'll provide two, though I was hoping I could avoid influencing people who answer here by not providing them: "balance on one's shoulder", "held/nestled/sandwiched between shoulder and ear". Shortest sequence containing all permutations Given an integer $n$, define $s(n)$ to be the length of the shortest sequence $S = (a_1, \cdots a_{s(n)})$ such that every permutation of $\{1,\cdots,n\}$ is a subsequence of $S$.  If $n=1$, then $S = (1)$ is the shortest sequence containing all permutations of $\{1\}$, so s(1) = 1.  If $n=2$, then $S = (1, 2, 1)$ contains all permutations of $\{1,2\}$ as a subsequence, so $s(2)=3$.  Is there a general formula for $s(n)$? How will old M42 lenses work on a Nikon camera?