For continuous functions, if they are equal on $\mathbb{Q}$ then they are equal on $\mathbb{R}$
Prove continuous functions $f$ and $g$ are equal
Is it possible to write a template that changes behavior depending on if a certain member function is defined on a class?  Here's a simple example of what I would want to write:  template&lt;class T&gt; std::string optionalToString(T* obj) {     if (FUNCTION_EXISTS(T-&gt;toString))         return obj-&gt;toString();     else         return "toString not defined"; }   So, if class T has toString() defined, then it uses it; otherwise, it doesn't. The magical part that I don't know how to do is the "FUNCTION_EXISTS" part. I have a simple shutdown script which i want to run as root  shutdown -h +30; echo "succesfull";   I have followed these answer, to make my script root.  first I run this command  sudo chown root.root $HOME/test/test.sh sudo chmod 4755 $HOME/test/test.sh   and then made changes in sudoers  sudo visudo   added this command after this line %sudo   ALL=(ALL:ALL) ALL  eka ALL=(ALL) NOPASSWD: $HOME/test/test.sh   But when i executed my script its showing this error  shutdown: Need to be root succesfull A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$ I  have had no luck getting the buffer tool to accept anything but degrees as units of measure.  I have found lots of stuff saying the layer needs to be reprojected and saved but it hasn't worked at all for me.   Is there a way I could create a buffer without using ftools or at least force the units to meters somehow?  As a workaround I converted meters to degrees (lat) and used that but the final product needs to be as close to reality as possible.  Things I've tried:   setting every unit option I could find to meters (where possible). setting everything to NAD83/Maryland (data is for Washington, DC) and saving it as such (as layers in ESRI shape files). reimporting the reprojected layers setting relevant layers to Google Mercator   The was tried followed by creating a buffer. Many were tried in combination. QGIS 1.7.3 Slackware64 current (qgis from SBo-13.37 repo, tried on multilib and plain 64it with same results) Python string prints as [u'String'] This will surely be an easy one but it is really bugging me.   I have a script that reads in a webpage and uses  to parse it. From the soup I extract all the links as my final goal is to print out the link.contents.  All of the text that I am parsing is ASCII. I know that Python treats strings as unicode, and I am sure this is very handy, just of no use in my wee script.   Every time I go to print out a variable that holds 'String' I get [u'String'] printed to the screen. Is there a simple way of getting this back into just ascii or should I write a regex to strip it? First Order Language for vector spaces over fields I'm attempting to come up with a first order language $L$ that is able to describe vector spaces over fields. I came up with a few sets of nonlogical symbols.  $Rs_L=\{Scal,Vec\}$ where $Scal,Vec$ are unary relation symbols which I interpret to be true or false depending on whether $x$ is a scalar or vector.  Also, $Fs_L=\{+,\cdot,\}$ which are the usual addition and multiplication for both vectors and scalars.  For constant symbols, $Cs_L=\{0,1,0_V\}$, where $0$ and $1$ are regular field scalars for the additive and multiplicative identities, respectively, and $0_V$ is the additive identity for vectors.   Using these, I was able to formulate axioms for scalar multiplication on a given structure, and I define addition between a scalar and a vector to simply always give the 0 vector and define multiplication between two vectors to always be the 0 vector. This gives a theory such that a structure models it if and only if it is a vector space in the regular algebraic sense. It is easy to see that all linear transformations in the algebraic sense are included in the class of homomorphisms (in the logical sense), but I am having difficulty proving they are the only ones in this class.   I suppose I want to show that for any $L$-homomorphism $T$, $T(av+w)=aTv+Tw$ for $a$ a scalar and $v,w$ vectors. Since $T$ is a homomorphism, I see that $T(av+w)=Tav+Tw=TaTv+Tw$, so it would be enough to show that all homomorphisms act as the identity on all scalars? Is there a way to show this, or an extra axiom to include? "There is/are more than one". What's the difference? While adding to an Answer to  question, I needed to use the above phrase, and I suddenly realised I was unsure whether to write "is" or "are".   There is more than one way to skin a cat. If there are more than one species of cat, we will flay each species differently.   I don't think that second example above sounds quite right to me (disregarding the meaning - sorry!), but in my original Answer I felt "is" would have been even worse.  Is "are" always wrong here? If so, what exactly is the rationale? If not, is there a case where it's unquestionably preferred – and why is that?    Note that in both the problematic Answer and my example attempting to mimic the same context more briefly, the writer doesn't know how many there are. There may be one, more, or even none.  Getting even more specific, the writer might have an opinion on how many there might be, and wish to convey his leanings by choice of verb form if language allows this to be done succinctly. How do you get vim to display wrapped lines without inserting newlines? I'm getting back in touch with my inner (g)vim due to an unscheduled MacBook mother(board) of a meltdown (my emergency backup Linux box won't run TextMate). All told I'm happy with vim's efficiency and power, but I'm mortified at how hard it is to get the kind of word wrap that even stupid HTML textareas achieve with no apparent effort.  Consider the text  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nullam.  By default, with an 80-character width vim displays this as  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nu llam.  This wrapping doesn't care about whitespace, so sometimes it just slices words into pieces (nullam in this case). Of course, you can turn on word wrap, and get this:  Etiam ornare mollis tortor. Suspendisse sed neque. Nullam in elit. Cum sociis nullam.  The problem is that vim inserts a newline at the linebreak, which I most emphatically do not want. In other words, I want the text to display exactly as vim displays it with word wrap turned on, but without inserting a newline. (This way it can be pasted into HTML textareas and email programs, among other places.)  Web searches have yielded nothing of use, despite diligent effort; I hope StackOverflow can succeed where my Google-fu has failed. Why does this sort ignore the +/- character prefix? What is the logical form of the definition of validity? My text book gives the definition of validity as "An argument is valid IFF if the premises are true, then the conclusion must be true". Using a conditional elimination on the RHS of the IFF yields "An argument is valid IFF the premises are false or the conclusion is true".   Yet, this seems strange to me. Am I doing something incorrect with my manipulation or is this definition actually true? Surely the criteria for a valid argument goes beyond a false set of premises or a true conclusion. What will reduce my rendertime? What would reduce the render time? Should I get a better GPU or more RAM? The normal JOIN ... ON ... syntax is well known. But it is also possible to position the ON clause separately from the JOIN that it corresponds to. This is something that is rarely seen in practice, not found in tutorials and I have not found any web resource that even mentions that this is possible.  Here is a script to play around with:  SELECT * INTO #widgets1 FROM (VALUES (1), (2), (3)) x(WidgetID)   SELECT * INTO #widgets2 FROM (VALUES (1, 'SomeValue1'), (2, 'SomeValue2'), (3, 'SomeValue3')) x(WidgetID, SomeValue)  SELECT * INTO #widgetProperties FROM (VALUES     (1, 'a'), (1, 'b'),     (2, 'a'), (2, 'b')) x(WidgetID, PropertyName)   --q1 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN #widgets2 w2 ON w2.WidgetID = w1.WidgetID LEFT JOIN #widgetProperties wp ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b' ORDER BY w1.WidgetID   --q2 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN #widgets2 w2 --no ON clause here JOIN #widgetProperties wp  ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b'  ON w2.WidgetID = w1.WidgetID ORDER BY w1.WidgetID   --q3 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN (     #widgets2 w2 --no SELECT or FROM here     JOIN #widgetProperties wp     ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b') ON w2.WidgetID = w1.WidgetID ORDER BY w1.WidgetID   q1 looks normal. q2 and q3 have these unusual positionings of the ON clause.  This script does not necessarily make much sense. It was hard for me to contrive a meaningful scenario.  So what do these unusual syntax patterns mean? How is this defined? I noticed that not all positions and orderings for the two ON clauses are allowed. What are the rules governing this?  Also is it ever a good idea to write queries like this? $\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime Why is a nonstop flight sometimes more expensive than multiple connections? Usually I find a flight I like that uses one or more connections with the same or different companies. In these cases, if the distance between the first and the second connection is not too large, I prefer to go by bus or train and then take the flight. The problem is that sometimes it is more expensive to take the flight in the second airport than to take the flight from the first one. I mean, I'm wondering why sometimes it is more expensive to take only a flight than to take the same flight and another one.  A practical example (and real, you can check with SkyScanner). Imagine I am in Madrid (Spain) and would like to go to Rio de Janeiro (Brazil) on April 1st. The cheapest flight I have found is this:     TAM airlines: MAD -> GRU -> GIG : 507 €   Fantastic! GRU is one of São Paulo's airports. That's perfect for me! I'll go on to Rio traveling overland. But then, I look for this flight (MAD -> GRU, non-stop):     TAM airlines: MAD -> GRU : 597 €   It's the same flight, 90 € more expensive! I've found this kind of behavior a lot of times and I'm intrigued to know why it happens. Reversing Drop Bars If I need to sit more upright on an old Fuji road bike, can I turn the drop handlebars upright and reversed so that they come up and then point to the rear?  I haven't seen anything on the net from anyone who has done that. Verb agreement with "what" This came up when reviewing a written English exercise, and I realized that I don't entirely trust my intuition on the answer.  Which of the following is correct?  Or are both valid?  (Or is it strongly advisable to rewrite the sentence in some other way?)   "I see what appears to be a man and his son." "I see what appear to be a man and his son." Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$ What does role db_owner allow I have been trying to troubleshoot a login that is not able to view certain tables in a SQL Server 2012 database. In doing so I find I don't quite understand what membership in the db_owner role allows. I can understand the other roles such as db_datareader and db_datawriter but I remain confused as to what db_owner allows. past simple or present perfect Please have a look at this sentence:     We haven't gotten a lot of Finnish groups that we liked here at Bananas but I'm pretty happy with this four tracker from Helsinki, apparently recorded in the same place where the Ramones played in the 70's.     The first verb is in present perfect (up to now) and the second is in simple past tense. I don't understand the simple past for the second verb.  Why "like" is not in its present perfect form as the first verb is? Copying unicode symbols from Firefox address bar as is Let's say I open a webpage with some Unicode characters, say, Cyrillic, in the address like this:        When I try to copy it from the address bar somewhere else, it becomes unreadable rubbish:        I guess this is for compatibility. However for readability I want to copy it straight away with proper Unicode characters.  What and how should I tweak to make that possible?  Edit: The answers are good, but they are hacky. Are there any settings in about:config?