What do we have to do when our question is resolved in the comments? Should we delete the question, or just let it appear as unanswered eternally, or there is another solution?  Edit:  I have read the question  but i think that the answer given by Kate Gregory would be also useful to the community as it suggests another solution which is not suggested in the first question.
I'm trying to go through and provide answers to every unanswered question (search &quot;closed:0 answers:0&quot;), somewhat following the spirit that was blogged about at  .  However, I'm finding this much more difficult than it needs to be, as many of the questions have already been answered without the use of an &quot;answer&quot; - but instead, in the form of a comment by either the OP or another poster. I wouldn't mind reading through and skipping these, as long as there was some appropriate action I could take to at least assist with preventing these questions from being seen again from the same query - either by myself or another SO member.  Is there such an appropriate action?  Should we vote to close?  If so, using what reason? Even if I vote to close, what are the chances that 4 other users will also view the question and also vote to close?  (i.e., will my individual vote even do any good?  Is there any report to show recent close votes, so that others may also review and contribute supporting close votes?) Should we post some sort of an answer - even just something to the effect of &quot;this was already answered by the OP's own comment to his answer (above)&quot;? Would something like this be appropriate to flag for moderator attention, and let the moderators deal with it?  (Or would this be considered too trivial?) Should we rename the question title to something standard that can be used in a search exclusion?  (Maybe &quot;SOLVED:&quot;?)  Basically, how can I help to denote questions as &quot;This question is no longer in active search of an answer - though better answers may still be appreciated.&quot;? I've already reviewed , which was closed as a duplicate of  - but this requires effort on part of a user who may very likely no longer be active. Otherwise, is there something I should be doing to improve my search to filter out these types of questions? I've run across this many times, so I don't consider it to be a rare issue.  However, the last question like this I just ran across, prompting this question, was .  In this case, the question was self-answered by the OP in the form of a comment, this question is the OP's only question, the OP has no other visible activity on SO, and the OP hasn't been seen on SO since he registered and posted the question 5 months ago. Another one I just ran across is .  However, here the &quot;answer&quot; comment was posted by a reputable and recently active SO member.  Should I leave a comment directed at him, asking him to re-post his comment as an answer, or should I post my own answer echoing his comment?  (Or something else?) Yet another is .  Interestingly, the OP actually self-edited the question to include the &quot;SOLVED:&quot; prefix on to the question, instead of posting his resolving comment as an answer (and ideally accepting it) as he was asked to do by another comment.  This brings up another good idea - is there a &quot;standard&quot; we should use to rename the titles on these &quot;resolved but unanswered&quot; posts that could be used as a search exclusion?  (Also added to the above list.)
"Where did you buy it?" or "where did you buy it from?" When someone purchase something from somewhere and I ask him the location of purchasing, which one is the correct question:     Where did you buy it?   OR     Where did you buy it from?   Is preposition necessary to use in this question or there is no need to use it? ubuntu 14.04 login loop problem Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$ I'm self studying from Category Theory in Context by Emily Riehl and have encountered the following question regarding slice categories:     Let $\text{C}$ be a category and $c$ be an object in $\text{C}$. Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$    The exercise appears in an chapter that introduces the notion of opposite categories and duality proofs.     My intuition of why the statement is true comes from the following observation:  Let $x,y$ be objects in $\mathbf{C}$ (or equivalently $\mathbf{C}^{\text{op}}$). Let $g^{\text{op}} : c \to y$ and $f^{\text{op}} : c \to x$ be objects in $c/(\mathbf{C}^{\text{op}})$. By the definition of slice category, there exists a morphism $h^{\text{op}} : y \to x$ in $\mathbf{C}^{\text{op}}$ such that the diagram below commutes:  $\hskip2in$   Now the 'corresponding diagram' in the opposite category $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ would be:  $\hskip2in$    which, as I understand it, would also be commutative. Now, to me, this indicates:   that the objects in $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ are the same as the objects in $\mathbf{C}/c$, namely, a morphism in $\mathbf{C}$ from an object $z \in \mathbf{C}$ to $c$. the commutativity of the seconds diagram describes morphisms $h$ in both $\mathbf{C}/c$ and $(c/(\mathbf{C}^{\text{op}}))^{\text{op}}$ if you reverse the arrows again you return to the same diagram. This makes me think you could construct a map between morphisms by first making a map from $ \mathbf{C}/c \to (\mathbf{C}/c)^{\text{op}} ( \cong c/(\mathbf{C}^{\text{op}}) )$ by $h \mapsto h^{op}$     Now, what I am really looking for is a way to structure a proof. I feel like I have some intuition but am very unsure of how to write it down in a concise way. I am new to category theory so I'm still very much learning how to construct these types of proofs using duality; I feel like what I have written is maybe overkill but I'm trying to be as explicit as possible to make sure I understand everything.  In particular, I don't know how I would get a concrete correspondence between morphisms in the two categories that respects associativity of composition etc.  Any help or pointers would be appreciated! A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$ I am not sure whether this is right. Can anyone verify, whether this proof is valid? Thanks!        Define a sequence $\{a_n\}_{n\ge0}$ as follows:   $$a_0=1,\qquad,a_1=3,\qquad,a_2=9,\qquad,a_n=a_{n-1}+a_{n-2}+a_{n-3}\text{ for }n\ge3.$$   Prove that for any positive integer $n$, $a_n\le3^n$.        Proof. Let $P(n)$: $a_n\le 3^n$, $n$ is a non-negative integer.      (i) Base case:         Consider when $n=0$. LHS$=a_0=1$, RHS=$3^0=1$ $\therefore$ LHS$\le$RHS, then $P(0)$ holds.   Consider when $n=1$. LHS$=a_1=3$, RHS=$3^1=3$ $\therefore$ LHS$\le$RHS, then $P(1)$ holds.   Consider when $n=1$. LHS$=a_2=9$, RHS=$3^2=9$ $\therefore$ LHS$\le$RHS, then $P(2)$ holds.         (ii) Inductive case:   Assume $P(i)$ is true for $0 \le i \le k$, $k\ge2$.      (iii) Inductive conclusion: Consider $n=k+1$.   $$ \begin{align*} \mathrm{LHS}=a_{k+1}&amp;=a_k+a_{k-1}+a_{k-2} \qquad\text{(by definition, since $k\ge 2$)}\\                     &amp;\le 3^k+3^{k-1}+3^{k-2} \qquad\text{(by Induction Hypothesis)}\\                     &amp;=3^k(3^{-1}+3^{-2}+3^{-3})\\                     &amp;=3^k\left(\frac13+\frac19+\frac1{27}\right)\\                     &amp;=\frac{13}{27} 3^k\\                     &amp;\le 3^{k+1} = \mathrm{RHS} \end{align*} $$   Therefore, by the Principle of Strong Induction, $P(n)$ is true for all non-negative positive integers $n$. How do I rename a directory via the command line? I have got the directory /home/user/oldname and I want to rename it to /home/user/newname. How can I do this in a terminal? Changing data type in ArcGIS attribute table? "Those who qualify will be awarded a certificate" or "those who qualify will be awarded certificates"? How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle? Using a transistor as a switch I am attaching a motor to an ATmega32 chip. I want to build an H-bridge but before doing that, I want to control the motor using the chip. I bought few NPN Transistors from RadioShack. I have 5V running though the breadboard. I attached Vcc to the Collector, Base to the Pin, and Emitter to the motor. And other wire of motor is hooked up to Ground. Unfortunately, the power coming out of the transistor is too low, the motor is barely moving (As opposed to when I hook up my motor straight to 5V). What is wrong? Do I need a different transistor or is my setup wrong? If it is the transistor, can you please recommend the right one, I am not too good at those. Follow a pipe using less? Can less follow (by pressing F) a piped input (similarly to a file)? For a file that is being written to, the command  less &lt;file&gt;   will follow the file when pressing F.  But if I have a command that pipes output directly into less, like this  command | less   pressing F will do nothing.  So it looks like pipes cannot be followed like files can? Or maybe it has to do with command also writing to STDERR? The effect I'm trying to achieve is always see the latest output of the command: just like keeping PageDown pressed!  A related remark holds for G (go to end): when piping directly to less, it won't work. How to stack three relations How can I add some html to my Mail.app signature? I want to add my company logo and and some juice to my contact information in the signature part in Mail.app. How can I do that with little or no efforts? How is every subset of the set of reals with the finite complement topology compact? While we know that every finite set is compact, how to prove that every infinite subset of $\mathbf{R}$, the set of all real numbers, is also compact in the finite-complement topology (also called the co-finite topology)?   What is the situation in the case of an arbitrary infinite set $X$ with the finite-complement topology? What's the best way of accessing field in the enclosing class from the nested class? If $F:M\to N$ is a smooth embedding, then so is $dF:TM\to TN$. I know that IList is the interface and List is the concrete type but I still don't know when to use each one. What I'm doing now is if I don't need the Sort or FindAll methods I use the interface. Am I right? Is there a better way to decide when to use the interface or the concrete type? How is unattended-upgrades started and how can I modify its schedule? I'm wondering who starts unattended-upgrades in my debian-jessie:   my man page   DESCRIPTION    This program can download and install security  upgrades  automatically    and  unattended,  taking care to only install packages from the config‐    ured APT source, and checking for dpkg prompts about configuration file    changes. All output is logged to /var/log/unattended-upgrades.log.    This  script  is  the backend for the APT::Periodic::Unattended-Upgrade    option and designed to be run from cron (e.g. via /etc/cron.daily/apt).  But my crontab doesn't show anything by crontab command:  @stefano:/etc/cron.daily$ crontab -l no crontab for stefano # crontab -l no crontab for root  But my unattended-upgrade work fine!(my unattended-upgrades log file) :  2017-02-05 12:42:42,835 INFO Initial blacklisted packages:  2017-02-05 12:42:42,866 INFO Initial whitelisted packages:  2017-02-05 12:42:42,868 INFO Starting unattended upgrades script 2017-02-05 12:42:42,870 INFO Allowed origins are: ['o=Debian,n=jessie', 'o=Debian,n=jessie-updates', 'o=Debian,n=jessie-backports', 'origin=Debian,codename=jessie,label=Debian-Security'] 2017-02-05 12:43:15,848 INFO No packages found that can be upgraded unattended   Where do I have to check/modify if I want to change my schedule? Let $\mathbb S = \varnothing$.      Then from the definition: $ \bigcap \mathbb S = \left\{{x: \forall X \in \mathbb S: x \in X}\right\}$      Consider any $x \in \mathbb U$.      Then as $\mathbb S = \varnothing$, it follows that: $\forall X \in \mathbb S: x \in X$ from the definition of vacuous truth.      It follows directly that: $\bigcap \mathbb S = \left\{{x: x \in \mathbb U}\right\}$      That is: $\bigcap \mathbb S = \mathbb U$. ()   Proofwiki uses the above "proof" to "prove" that intersection of the empty set is the whole universe.   My question is, is the use of vacuous truth really allowed in axiomatic set theory, like ZFC? I don't see how the use of vacuous truth is justified.   The next problem I can think of is that we cannot really "define" the elements of empty set (to my knowledge, there is no element in empty set) so how can we then prove as the above proof did? This seems to contradict the use of vacuous truth.  And of course, there is issue of using the whole universe as a set, and I don't think this is allowed.... (Maybe proof above is using a different axiomatic set theory, as I am using ZF-minded thoughts...) Installing PHP 5.3 in Ubuntu 14.04 How to fade one material into the other? Hello blender community.  Could someone please let me know how to fix this issue? I have one material for the whole face and a different one for the lips.  there's a noticeable edge that I want to get rid of. I just want it to have an ease fade instead of a sharp edge.   what's the best way to go about this?  Thank you in advance!    Finished Update  I wanted to give an update on how it was fixed with @hexbob6 and @Lemon 's help.    I needed two textures. One is the actual colored version and the 2nd is the black and white masked version. Hexbob6 described very well on the process here:   A: The node process on how to do it.    The B/W masked texture is going to be connected to the Fac of the mixed shader along with its UV coordinates. Make sure the image is on clip instead of repeat. the 1st shader is going to be the black part of the B/W masked texture. An important thing to note is if you have a texture already for the object, be sure to connect the other UV coordinates! the 2nd shader will be the white part of the B/W masked texture.   B: This section is the UV layout called "mainUV" where all the color goes.  C: This section is the B/W masked texture to focus on the lips.  D: Just the render view  E: Best way to texture something is to be able to see it in 3D view and texture paint.  F: Just showing that there are two textures to keep track of. One is the main UV and the 2nd is to focus on the lip.   That was it. Once again thanks to those who replied and helped me figure this problem. In the process I learned other things that I didn't know about blender even though I've been using it for years.