Continuous linear operator with noncontinuous inverse
Open Mapping Theorem: counterexample
How to use iSight webcam without activating the green light? Recently a the Dutch government advised to put a tape on your webcam to prevent hackers from taking pictures and video using your device ().  The build in iSight camera in Apple laptops have a green light next to the camera, this light turns green when you use the camera.  Is it possible to use the camera without the activation of the green light? Personally I think the green light turns on when the sensor requires power and this is hardwired in the hardware. Am I wrong?  I have found similar questions on stackexchange, but I found non that answer this specific question. Can anyone come up with an explicit example of two functions $f$ and $g$ such that: $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective?  I tried the following: $$f:\mathbb{R}\rightarrow \mathbb{R^{+}} $$ $$f(x)=x^{2}$$  and  $$g:\mathbb{R^{+}}\rightarrow \mathbb{R}$$ $$g(x)=\sqrt{x}$$  $f$ is not injective, and $g$ is not surjective, but $f\circ g$ is bijective  Any other examples? Windows Logs Application is full of "Login failed for user 'sa'. Reason: Password did not match that for the login provided. [CLIENT: ****]" I have Windows Server 2016, with SQL Server 2017, and found Windows Log Application is full of Login failed messages (as follows) :     Login failed for user 'sa'. Reason: Password did not match that for the login provided. [CLIENT: ****]    Client's IP addresses are various. I don't have any maintenance plan in SQL Server     What's the problem? In my game, XP needed to reach the next level is Current Level × Level Threshold.  Given that, how can I get my current level from the total XP ever earned?    For example:  Level Threshold = 50 Current Level = 1   Starting at level 1, I would need (1 × 50) = 50 XP to get to level 2, and so on.  Level 1: 50 XP needed to reach level 2 Level 2: 100 more XP needed to reach level 3 Level 3: 150 more XP needed to reach level 4   In other words, the progression table is as follows:  Level 1: 0 XP to 49 XP Level 2: 50 XP to 149 XP  Level 3: 150 XP to 299 XP Level 4: 300 XP to 499 XP   If I have 300 XP, I'll just reached level 4. How can I calculate that generally? I can't (vote to) close a question I voted to close before but then retracted? For example...  I closed a vote for 'too broad'. But then I realized I wanted to close it as a specific duplicate of another question instead. So I retracted my close vote.  That worked. But I can't now vote to close as duplicate and the title says I already voted to close.  Maybe this is intentional but it doesn't feel that way. How can I see the history of stories I've read on Apple News? Sometimes I'll be interrupted in the middle of reading a story on Apple News and later when I open the app, it didn't save the story I was previously reading. I want to be able to resume reading the article, how can I find it again? No sound (speakers/jack) + microphone's dead after spilling water Down vote changed to up vote caused reputation meter to pass daily maximum I just experienced a minor visual bug.  I had an answer that earned 2 down votes and 22+ upvotes, earning me the daily maximum of +200. Upon making some edits to the answer at the behest of the comments, one of the users who down voted changed their vote. Now my reputation meter shows that I gained +202 for the day.    This correctly did NOT affect my reputation, as I still only gained 200, so it is merely a minor display bug.  This appears in the achievements drop down and my reputation tab on my profile. If $xy + yz + zx = 1$, then show that      $$\dfrac{x}{1-x^2} + \dfrac{y}{1-y^2} + \dfrac{z}{1-z^2} = \dfrac{4xyz}{(1-x^2)(1-y^2)(1-z^2)}$$   I tried doing the sum algebraically, that is, by solving the LHS but, that method isn't really getting us anywhere.  Also, I found this sum in an a book on trigonometry. So how can I solve it with trigonometry? To illustrate, assume that I have two tables as follows:  VehicleID Name 1         Chuck 2         Larry  LocationID VehicleID City 1          1         New York 2          1         Seattle 3          1         Vancouver 4          2         Los Angeles 5          2         Houston   I want to write a query to return the following results:  VehicleID Name    Locations 1         Chuck   New York, Seattle, Vancouver 2         Larry   Los Angeles, Houston   I know that this can be done using server side cursors, ie:  DECLARE @VehicleID int DECLARE @VehicleName varchar(100) DECLARE @LocationCity varchar(100) DECLARE @Locations varchar(4000) DECLARE @Results TABLE (   VehicleID int   Name varchar(100)   Locations varchar(4000) )  DECLARE VehiclesCursor CURSOR FOR SELECT   [VehicleID] , [Name] FROM [Vehicles]  OPEN VehiclesCursor  FETCH NEXT FROM VehiclesCursor INTO   @VehicleID , @VehicleName WHILE @@FETCH_STATUS = 0 BEGIN    SET @Locations = ''    DECLARE LocationsCursor CURSOR FOR   SELECT     [City]   FROM [Locations]   WHERE [VehicleID] = @VehicleID    OPEN LocationsCursor    FETCH NEXT FROM LocationsCursor INTO     @LocationCity   WHILE @@FETCH_STATUS = 0   BEGIN     SET @Locations = @Locations + @LocationCity      FETCH NEXT FROM LocationsCursor INTO       @LocationCity   END   CLOSE LocationsCursor   DEALLOCATE LocationsCursor    INSERT INTO @Results (VehicleID, Name, Locations) SELECT @VehicleID, @Name, @Locations  END      CLOSE VehiclesCursor DEALLOCATE VehiclesCursor  SELECT * FROM @Results   However, as you can see, this requires a great deal of code.  What I would like is a generic function that would allow me to do something like this:  SELECT VehicleID      , Name      , JOIN(SELECT City FROM Locations WHERE VehicleID = Vehicles.VehicleID, ', ') AS Locations FROM Vehicles   Is this possible?  Or something similar? I made a Yu-Gi-Oh card but it is not broken like current broken Yu-Gi-Oh cards and here it is to see but please before you make your decision about it take another look on ''dragun of red eyes''. I want to do:  int a = 255;  cout &lt;&lt; a;   and have it show FF in the output, how would I do this? How to install Ubuntu on VirtualBox? Is the function strcpy always dangerous? $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational Prove that $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational.   I would assume that $\sqrt[31]{12} +\sqrt[12]{31}$ is rational and try to find a contradiction.  However, I don't know where to start. Can someone give me a tip on how to approach this problem? Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$ Paucity of words for relationships SELECT name, gdp/population as capita  FROM world w1  WHERE continent = 'Europe'       AND capita &gt;  (     SELECT gdp/population      FROM world      WHERE name = 'United Kingdom' );   How come I can't refer to capita in the WHERE clause? It returns this error:  Unknown column 'capita' in 'where clause'   I can however, run the query if I replace capita with gdp/population.  I don't want to do gdp/population &gt; .... How can I do capita &gt; ...? Or is this not possible? Deleting Objects in JavaScript LM317 Heat sink, how big?