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How to prove that $d \sin(x)/dx = \cos(x)$ without circular logic such as L'Hôpital's rule? Notation for intervals I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed . I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall someone calling the notation with $[a,b]$ and $]a,b[$ as French notation.   What are the origins of the two notations?  Is the name French notation correct? Are they used frequently in France? Or were they perhaps prevalent in French mathematical community at some point? (In this  Bourbaki is mentioned in connection with the notation $]a,b[$.)      Since several answerers have already mentioned that they have never seen $\langle a,b \rangle$ to be used for closed intervals, I have tried to look for some occurrences for this. The best I can come up with is the article on , where these notations are called Czech notation and French notation. Using $(a,b)$ and $[a,b]$ is called English notation in that article. (I am from Central Europe, too, so it is perhaps not that surprising that I have seen this notation in lectures.) I also tried to google for  or . Surprisingly, this lead me to a  where this notation is used for open interval. Will I lose previous purchases when I change country in iTunes Mobile site says "your answer couldn't.." when submitting a question edit that creates a new tag Noticed this on Bicycles, but I presume it affects any Stack Exchange site   Write question Edit question, write a new tag Submit edit   When performing the above steps, I properly get an error message, but it says "answer" instead of "question" or "edit". WHERE IN (array of IDs) I have webservice which is passed an array of ints. I'd like to do the select statement as follows but keep getting errors. Do I need to change the array to a string?  [WebMethod] public MiniEvent[] getAdminEvents(int buildingID, DateTime startDate) {         command.CommandText = @"SELECT id,                             startDateTime, endDateTime From                             tb_bookings WHERE buildingID IN                             (@buildingIDs) AND startDateTime &lt;=                             @fromDate";      SqlParameter buildID = new SqlParameter("@buildingIDs", buildingIDs); } If two vectors $a$ and $b$ make angle $\alpha$ and $\beta$ with the $x$-axis, prove, using vectors, that:   $$\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$$   I tried taking components of each vector along the plane, but that didn't get me anywhere. I tried taking component of vector $b$ along vector $a$, but I also got stuck there. Can anyone point me in the right direction? What happens if you use a Clone Effect on a Double Faced Card that's Transformed? Say someone has , which is a 0/3 Defender, and after some mechanics, transforms into a 13/13 Lizard Horror with Trample.  Say this someone managed to transform said card into its 13/13 Trample form, and then cast  on it (or any other clone type card if it would matter between different ones). Does the Metamorph/Clone/etc. come into play transformed, or as the 0/3 Defender? I was told that the following does not work:     Employees having children will be granted a day off.   However, this sounds better:     Having children, those employees will be granted a day off.   What is wrong with the first clause? Initial capitalization of foreign surnames when starting a sentence How to allow to run su instantly after I added the user to the appropriate group Evaluate the limit: $$\mathop {\lim }\limits_{x \to \infty } x\left( {{{\left( {1 + {1 \over x}} \right)}^x} - e} \right)$$  My attempts didn't yield a result. I'd be glad for a guidance. Thanks! How to create a database directory structure for MySQL? Change the Python3 default version in Ubuntu I am using Ubuntu 16.04 LTS . I have python3 installed. There are  two versions installed, python 3.4.3 and python 3.6 . Whenever I use python3 command, it takes python 3.4.3 by default. I want to use python 3.6 with python3. python3 --version shows version 3.4.3 I am installing ansible which supports version &gt; 3.5 . So, whenever, I type ansible in the terminal, it throws error because of python 3.4 sudo update-alternatives --config python3 update-alternatives: error: no alternatives for python3 The reason that I ask is because this is happening to LiDAR, and I am inclined to use lidar because it is easier to read. Google chrome is reading characters backwards Google Chrome is my favorite browser, and I can't imagine going on without it. Suddenly (without closing and re-opening) the browser; chrome has been reading characters upside down, very weird:    Chrome version:    I tried restarting my browser and my MAC (running OS X Yosemite 10.10), but the error keeps on coming. "Stack Overflow requires external JavaScript from another domain" message Why there is "the" before some names but not others Is there a rule beyond the common "no the with proper nouns and names" for the following problem?     I saw the Empire State Building.      We went to the White House.      We saw the Golden Gate Bridge.   but     I went to Death Valley National Park.      I crossed Brooklyn Bridge. Let $G$ be a group and $H$ be a normal subgroup of index $p$ ( a prime ) ; suppose $K$ is a subgroup of $G$ not contained in $H$ , then is it true that $G=HK$ ? ( I know that the fact is true if $p=2$ , but I don't know for the general case . Please help . Thanks in advance ) Could Hermione really free the Hogwarts house-elves with her knitted hats? Getting key with maximum value in dictionary? I have a dictionary: keys are strings, values are integers.  Example:   stats = {'a':1000, 'b':3000, 'c': 100}   I'd like to get 'b' as an answer, since it's the key with a higher value.  I did the following, using an intermediate list with reversed key-value tuples:  inverse = [(value, key) for key, value in stats.items()] print max(inverse)[1]   Is that one the better (or even more elegant) approach?