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Prove that $g$ is tangent to the graph of $f$ During Winterbash 2014, there was a hat called , which was earned by giving an answer scoring 5 or better to question that had a score of −3 or worse at the time of answering and later rose to a score of +3 or better.  I’ve already shared the . Those cases give me a great deal of confidence that this would be a challenging badge trigger that would produce good behavior with a minor tweak. Here are the Red Barons earned on other sites:    (Logan Maingi) Mathematics  (Mike Miller) Mathematics  (Hugo) English Language and Usage  (tchrist) English Language and Usage  (Mr. Shiny and New 安宇) English Language and Usage  (Darth Satan) Science Fiction and Fantasy  (DVK) Science Fiction and Fantasy  (rolfl) Code Review  (Heslacher and Hosch250) Code Review  (Edward) Code Review  (janos and Manny Meng) Code Review  (Mark Mayo, Rory Alsop and MeNoTalk) Travel      (DJClayworth) Christianity  (McMagister) Puzzling   Looking through the timelines, I’m convinced that the answerer’s votes should be excluded from the pre-answer question score calculation. Doing that would have reduced the number of Red Barons to 16 across the network. However, the cost of making a badge harder to obtain is worth the benefit of avoiding giving people an incentive to manipulate question scores¹.  To wrap up, the hat seemed to have encouraged a number of great answers and rescued some questions that would otherwise have been lost to time. My outstanding questions are:   Were there any problems on questions where people were attempting to earn the hat, but failed? (Or any other problems I didn’t observe.) If not, should we  or create a new badge? If we create a new badge, what should it be called?   I’m especially interested in feedback that counters my own bias in favor of this idea. If I’m missing any problems, I’d like to know about them now.    ¹ Several questions were downvoted, answered, edited (sometimes trivially)  and upvoted by the user who earned the hat. I was wondering if there is a name for a function that satisfies the conditions  $f:\mathbb{R} \to \mathbb{R}$ and $f(x+y)=f(x) \cdot f(y)$?  Thanks and regards! How to automatically rotate images based on EXIF data? Iterate a list as pair (current, next) in Python Where is the denoiser? How to prove that $L=${$a^p$: p is prime} isn't regular? I tried using pumping lemma or finding infinite equivalence classes, but I didn't succeed.  It's clear to me that there is no automata that accepts this language, but I just can't formally prove that this language isn't regular.  How can you prove it? What component to use for audio signal switching? I'm looking to build a guitar pedal switcher based on a Raspberry Pi or Arduino (have not yet decided, but I have an unused Raspberry around and I lean towards that). Anyway, digital logic.  Now, I need to switch audio signal obviously and I need to do it quietly (both physical silence and electrical silence). Please note that the signal is line level throughout most of the build, except for the input which is much lower. I will probably have 2 or 3 loops before the preamp so those may not encounter line level signal.  From what I read and know, so far, mechanical relays are not really an option due to the clicking noise they make. I also read something about FETs, but that's a bit out of my league and I would appreciate any info on these.  PS: I will probably use different power rails for the digital and analog paths.  PS2: The whole thing will be mounted in a 1U rack enclosure, so please tell me if I should take into consideration any thermal issues. I eliminated a computer player that had a strong religion (Buddhism). My religion was weak, whereas this other one was taking over the continent quickly. Now that I have him overrun, I want, well wanted, to work on converting cities to mine, but I see now that all of the cities period have his religion! I tried making an Inquisitor just to test, but he is ineffectual at removing Buddhism, being that I can only buy him in Buddhist cities. (Because all of my cities are Buddhist and my religion, Shinto, has been wiped out.   Is there no way to recover your religion in such a situation? Is there a dollar amount that, when adding Massachusetts Sales Tax, precisely equals $200? I am just curious, I use handlebar mounted lights, and since I have multiple bikes to switch, it's a lot of trouble changing the light from one to another. So, I am thinking of switching to helmet mounted lights.  Give me your point of view. Why or why not? Which is better suitable for which riding type? Physics history book with some math I am looking for a book explaining physics from, say, Galileo and Newton till now; the book should be written using some math, similarly to my physics books when I was at the university (Halliday Resnik). I am searching a book that take care of explaining the true "evolution" of reasoning, discoveries, experiment to prove or disprove something.  I do not like a book that gives definitions without explaining what had happened. I also like to find, on that book, explanations on how actual measurements are taken (how can we measure the speed of light, the mass of celestial bodies, the attributes of electron, and how were the measurements taken in the past - how was possible to measure the speed of light in 1700-1800?).  I am not very interested in recent theories like strings, branes.... so it is OK if these are not discussed.  I like to find a lot of discussions on concept that are related, like for instance the implications on space dimensionalities, ether non-existence, strange facts, missing explanations. I would like to prove that : If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then  $$|G:K|=|G:H||H:K|$$  I appreciate any clear explanation of this. Thanks ! How do I make the method return type generic? Consider this example (typical in OOP books):    I have an Animal class, where each Animal can have many friends. And subclasses like Dog, Duck, Mouse etc which add specific behavior like bark(), quack() etc.  Here's the Animal class:  public class Animal {     private Map&lt;String,Animal&gt; friends = new HashMap&lt;&gt;();      public void addFriend(String name, Animal animal){         friends.put(name,animal);     }      public Animal callFriend(String name){         return friends.get(name);     } }   And here's some code snippet with lots of typecasting:  Mouse jerry = new Mouse(); jerry.addFriend("spike", new Dog()); jerry.addFriend("quacker", new Duck());  ((Dog) jerry.callFriend("spike")).bark(); ((Duck) jerry.callFriend("quacker")).quack();   Is there any way I can use generics for the return type to get rid of the typecasting, so that I can say      jerry.callFriend("spike").bark(); jerry.callFriend("quacker").quack();   Here's some initial code with return type conveyed to the method as a parameter that's never used.   public&lt;T extends Animal&gt; T callFriend(String name, T unusedTypeObj){     return (T)friends.get(name);         }   Is there a way to figure out the return type at runtime without the extra parameter using instanceof? Or at least by passing a class of the type instead of a dummy instance. I understand generics are for compile time type-checking, but is there a workaround for this? I'm trying to find a good way to print leading 0, such as 01001 for a . While the number would be stored as 1001, what is a good way to do it? I thought of using either case statements or if to figure out how many digits the number is and then convert it to an char array with extra 0's for printing, but I can't help but think there may be a way to do this with the printf format syntax that is eluding me. How do I write a cpp macro which expands to include newlines? I got quite some trouble trying to prove this.  $$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n&gt;m\geq 0$$  I tried using $$\binom{n}{m}\binom{m}{k}=\binom{n}{k}\binom{n-k}{m-k}$$ and then changing the summation boundaries as $k=0, n=n-m$, but that took me nowhere... I would really appreciate help. Thank you. How to make left-right transition of overlay image ffmpeg Is a 2-hour transit time enough to catch a connecting flight in Muscat airport? Both flights are with Oman Air I am flying from Dubai to India with Oman Air with a layover of 2 hours at Muscat airport. Is 2 hours enough for me to catch my connecting flight from Muscat to New Delhi? My flight from Dubai to Muscat as well as the connecting flight from Muscat to New Delhi are with Oman Air. Do I need to re-check in my luggage? Am I taking a risk or should I take an earlier flight from Dubai to get more layover time to be on the safer side? So I just got this Nikon D3100 Camera.  And I am trying to take a picture using autofocus with the kit lens(18-55mm).    The system is in Auto mode, AF-A, single frame and the lens A-M switch is on "A",  VR is "ON".  When I press shutter half way down, focus confirmation light in lower left corner of viewfinder neither lit nor blinks(hear clicking). When I press the shutter all the way down, the shutter seems locked (hear clicking, but shutter not released).    The manual says the shutter will lock itself if it can't get focus. But the place is well lit and have distinct color and I can easily focus using my old Canon.    The camera works fine in manual focusing, but I can't get it to take picture under auto-focusing.  I wonder is there something wrong with the setting that I don't know or is that I got a lemon?  Thanks