I was quite early with registering my Gmail account and I got a nice and clean baker@gmail.com address. Apparently all mails end up on my account when people make simple mistakes in typing the intended e-mail address. So I receive several legitimate mails each month from people that did not intend to mail me; people that I don't know and have no desire to know.  If it where snail mail, I'd write Undeliverable or Wrong address over the envelope and put it back in the outgoing mail box. Now I'm looking for a way to do the same for e-mail.   How can I show the sender of an e-mail that the e-mail address is wrong without revealing my identity?  Any solution involving a Gmail feature, third-party application, or manipulation of the SMTP protocol is acceptable (I can program it if it doesn't exist already), as long as it works from Windows.    I used to reply along the lines of: You sent this e-mail to the wrong address. You sent it to baker@gmail.com but you probably meant baker1@gmail.com. Kind regards, Marilyn Baker, revealing that my e-mail address is valid and who I was, and then they'd reply: Hey you have the same surname. You guys must surely be distantly related. Bla bla bla... John Baker is my husband, let's meet up... Bla bla. Anna Baker-Field  All names and e-mail addresses are fake.
Prima facie this is impossible but perhaps someone has some kind of hack to do it. This is one of the last things holding me back from switching to Gmail from Pine.  To be clear, bouncing a message is like forwarding but leaving all the headers intact. It sort of amounts to spoofing the email, which perhaps is why Gmail doesn't support it. To the recipient of a bounced email, it seems as if they were just BCC'd.
At what moment will matter falling into a black hole affect its size? Does the mass of matter falling into a black hole affect the size of an event horizon the moment it passes through it, or when it has been incorporated into the singularity? I've heard that in the study of finite fields, and other concepts related to finite fields, mathematicians have found a sort of gap: there are various results and things that seem like they correspond to a field with one element, $\mathbf{F}_1$, even though there is no such field. Of course, there is an object which seems similar to a field with one element: the zero ring, $\mathbf{Z}_1$, defined as having one element, $0$, obeying the equations $$0 + 0 = 0 - 0 = 0 \cdot 0 = 1 = 0.$$ The zero ring seems to behave like a field in every respect, except for the fact that it fails to satisfy $0 \ne 1$. (But the importance of the axiom $0 \ne 1$ isn't clear to me.) However, in any case, there seems to be consensus that the zero ring is not the field with one element. People say that the zero ring &quot;does not behave like a finite field&quot; () or that it &quot;does not have the features that mathematicians need&quot; (). I'm not familiar enough with algebraic geometry to understand the properties that $\mathbf{F}_1$ is expected to have. Is there an elementary, undergraduate-level explanation of  why it seems like a field with one element &quot;ought to exist&quot; in the first place, what properties we expect it to have and why, and how the zero ring fails to satisfy these properties?  Or do I need to study algebraic geometry if I want to have an understanding of any of this? (A side question: do we have a good answer to the question of whether the single element of $\mathbf{F}_1$ ought to be $0$, $1$, both, or neither?) How do I bypass "this connection is not private" warnings in safari? Matrix in a matrix I would like to draw a matrix with top left, top right, bottom left and bottom right blocks. The top left should be a 3x3 matrix with numerical entries, the top right is 0, the bottom left is 0 and the bottom right is just a "single" entry uJ. Here is my attempt.    $ \left[ \begin{array}{c|c} [\begin{array{c|c|c} 0 &amp; 0 &amp; 2\mathrm tr(MM^{*}) \\ 0 &amp; 0 &amp; -ua \\ u &amp; -ua &amp; 0 \end{array}]     &amp;  0\\ \hline 0 &amp; uJ  \end{array}\right]. $    I would like to emphasize that the non-top-left entries are not just single entries, but blocks, so I do not want to just make a 4 by 4 matrix with vlines and hlines and additional 0's. Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$. After working it out on a number line, I got: $\{4, 5, 6\}$.  As it stands, the expression contains the integers that do not belong to the set $B$ that cross into $C$. This would result in $4, 5, 6$. Number $7$ would not be included because of the soft brackets surrounding $C = (2, 7)$. Is this correct? How should I deal with becoming discouraged as a graduate student? I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia? Probability of winning the game "1-2-3" Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta&gt;0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof. Confirm and agree to negative questions Redirect a portion of a bash script to a file to capture set -x output My host is x64 bits Windows 8.1.  I downloaded the latest Virtual Box (4.3) and I'm trying to create a VM with a 64 bits Ubuntu OS (ubuntu-12.04.3-desktop-amd64).  When I go to New VM wizard, it doesn't give me option to select "Ubuntu (x64)" as I have seen in other people's screenshots, only just "Ubuntu". As a result, the ISO can't boot. I tried in another PC and Virtual Box gives the x64 variants to most listed OS...  Control Panel shows x64 OS, x64 processor. My host laptop is a Sony Vaio VPCZ22UGX/N, Intel® Core™ i7-2640M processor. CPUz shows Vx-t is available on my processor, of course.  Here is what I tried so far:   I enabled IO APIC as required in the docs. I have virtualization enabled in the BIOS. It works fine in VMware. Check that Hyper-V is not running or even installed on my Windows. Same for VMware. I also tried running the command:  VBoxManage modifyvm [vmname] --longmode on    for that VM, but no change.. I think the issue is really that I can't select x64 variant of the Ubuntu OS for that VM. Other people seem to indicate that's a requirement, but I don't get that option for some reason.  I spent a lot of time and can't find what's wrong... Anyone knows what could be missing here?  Thank you very much!!  Eduardo avoid space after commas used as thousands separator in math mode Do we know how Senju Hashirama died? What would be the easiest way to view classes, methods, properties, etc. inside a jar file? I'm looking for something equivalent to the very useful  Lutz Roeder .NET Reflector  - for Java Assuming I have an ArrayList  ArrayList&lt;MyClass&gt; myList;   And I want to call toArray, is there a performance reason to use  MyClass[] arr = myList.toArray(new MyClass[myList.size()]);   over  MyClass[] arr = myList.toArray(new MyClass[0]);   ?  I prefer the second style, since it's less verbose, and I assumed that the compiler will make sure the empty array doesn't really get created, but I've been wondering if that's true.  Of course, in 99% of the cases it doesn't make a difference one way or the other, but I'd like to keep a consistent style between my normal code and my optimized inner loops... Hyperlinks clicked in evince document viewer are not opening, any ideas on how to fix? As it was instructed in another thread here in the forums, I opened the /usr/share/applications/mimeinfo.cache file to check for correct references. And noticed this doesn't seem to be the problem, there even are 3 optional browsers to use.  x-scheme-handler/http=google-chrome.desktop;chromium-browser.desktop;firefox.desktop; x-scheme-handler/https=google-chrome.desktop;chromium-browser.desktop;firefox.desktop;   I already checked that the programs are correctly named, using the "which" command in the terminal, like this:  $ which google-chrome $ /usr/bin/google-chrome   So google-chrome should be the first option and yet the order to open a url doesn't seem to be arriving to the program, not even to the 2nd or 3rd option for that matter anyways.  Also, the 'Get help online...' command in the 'Help' menu doesn't work. So it is not a problem with the specific document file either.  I'm running Ubuntu 12.04 LTS. If you need to ask for more relevant details, please do. It would be nice to have various opinions on how to solve this, thank you :-)  UPDATE: I ran evince from the terminal as asked. This is what I'm getting when trying to open a link:  /opt/google/chrome/google-chrome: line 42: /opt/google/chrome/chrome: Permission denied /opt/google/chrome/google-chrome: line 42: /opt/google/chrome/chrome: Success   Should I try the fix you suggested even if my error log is different?  UPDATE: Tried @maggotbrain's solution and BINGO, now I can study pdf references faster thanks to you bro! How does wizard & cleric spell preparation and casting work? In 3.X wizards had spellbooks, while clerics had their entire spell list, but they both memorized/prepared spells every day from those lists, and had a certain number of slots for preparing spells in.  Now in 5e preparing spells and spell slots aren't the same thing. What's going on here? How does their spellcasting work now? I want to use Google Chrome and Google search instead of Bing when I search in Windows 10.   Google Chrome is launched when I click on web, but it's Bing search. (My default search engine on Google and Edge is )    I haven't found how to configure that.  Someone can help me ? What element saved Iron Man from his blood poisoning? I just watched Iron Man 1&amp;2 the other day. I'm new to the entire story. In IM2 we learn that his blood is being poisoned and that he has tried every combination of every existing element as a cure - unsuccessfully. Then he deducts &quot;the key&quot; from the Expo park's plans which saves him. What is that key? What element had he not tried? I realize that the movie story has to be simplified, compared to the original story, so there are probably story elements that I have completely missed because they're only in the original works. We also saw that in LOTR. I am trying to write a condition into a SQL WHERE clause that forces the column comparison to a variable to be compared in lowercase. However the addExpression function isn't accomplishing this (since that is putting the expression in the field selection, not the where clause.  Here is what I have tried:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $query-&gt;addExpression("LOWER(ttd.name) = $category"); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;execute()     -&gt;fetchAssoc();   And this:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;condition('LOWER(ttd.name)', $category, '=')     -&gt;execute()     -&gt;fetchAssoc();   The second one becomes invalid and the first one causes the problem I mentioned above. Any thoughts or suggestions?  Thanks, Patrick