How small should functions be?
When is a function too long?
"One of the children who was" vs. "one of the children who were" In the construction "one of the [plural noun] who ...", should the verb agree with "one" or "[plural noun]"?   For example, which of the two following sentences is grammatically correct? Or are both acceptable?        She was one of the several children who was sold at the auction    She was one of the several children who were sold at the auction. What is the closure of an open ball $B_X(\mathbf{a},r)$ in $X=\mathbb{R}^n$? Suppose we have the open ball $B_{X}(\mathbf{a},r)$ and the closed ball $\bar{B}_{X}(\mathbf{a},r)$ of radius $r$ about $\mathbf{a}\in\mathbb{R}^n=X$ with the Euclidean metric $d_2$.  What is the closure of an open ball $B_{X}(\mathbf{a},r)$ in $(\mathbb{R}^n,d_2)$?  First, I have defined the sets like this:  $$B_X(\mathbf{a},r)=\{\mathbf{y}\in\mathbb{R}^n:d_2(\mathbf{a},\mathbf{y})&lt;r\}$$ $$\bar{B}_X(\mathbf{a},r)=\{\mathbf{y}\in\mathbb{R}^n:d_2(\mathbf{a},\mathbf{y})\le r\}$$  Then, let $U=B_X(\mathbf{a},r)$ and claim the closure is $$\bar{U}=\{\mathbf{x}\in\mathbb{R}^n:\exists (\mathbf{x}_n)\in U\text{s.t}~\mathbf{x}_n\to \mathbf{x}\}=\bar{B}_X(\mathbf{a},r).$$  Since closed balls are closed then we have $$\bar{U}\subset\bar{B}_X(\mathbf{a},r).$$  But, how can I prove the other direction $\bar{B}_X(\mathbf{a},r)\subset\bar{U}$?  Since it's a containment argument I know that I have to take any element from $\bar{B}_X(\mathbf{a},r)$ and show it is in $\bar{U}=\{\mathbf{x}\in\mathbb{R}^n:\exists (\mathbf{x}_n)\in U\text{s.t}~\mathbf{x}_n\to \mathbf{x}\}$.  But I do not know how to get an expression for $\mathbf{x}_n$.  I would appreciate any help. Set multicolumn width to default table width Paying off student loan or using that money for a downpayment on a house Should I really have been awarded mortarboard on a Per-site meta? Can anybody please suggest how I can compute the moment generating function of the inner product of two Gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each other? Is there some standard result available for this? Any pointer is highly appreciated. Git SSH error: "Connect to host: Bad file number" How to get Debian codename without lsb-release I am trying to create a script that requires me to print the debian codename so that I may echo it into the sources.list file.  I am trying to make this script work across any version of Debian, so I had hoped to set a bash variable of the release codename. This would be simple to do (with lsb_release -c), however our deployment images do not contain lsb_release by default - and with this script being required to fix the sources.list, installing lsb-release with apt-get would not be an option.  I have found numerous ways to get the release number and other info about the system, but cannot find a reliable place to get the codename.  Any ideas would be greatly appreciated!  (OS I am testing this with is Debian Squeeze) Inspired by a StackOverflow question ().  Is there a DBMS that actually supports the = NULL syntax? Why is energy in a wave proportional to amplitude squared? For Christmas my kiddo got the D&amp;D Starter Set and we've been going though it and the full rules we downloaded online. I'm having a hard time figuring out how the example listed in the rules gets to a final value of 14.  The example is a level 1 character with wisdom of 15 and a proficiency in perception.  I understand that you start with  10 (base) + 2 (character level) + 2 (wisdom 15) which gets you to 14 but then how does the "proficiency in perception" help or factor in?   What gets more confusing is on one of the pre-generated character sheets has a level 1 character with wisdom of 10 but a passive perception value of 10. If I follow the math from above shouldn't it be 10 (base) + 2 (char lev 1) + 0 (wisdom 10 = 0 bonus) for a final score of 12?  How to calculate passive perception? NullReferenceException in Unity Since many users are facing the NullReferenceException: Object reference not set to an instance of an object error in Unity, I thought that it would be a good idea to gather from multiple source some explanation and ways to fix this error.  Symptoms I am getting the error below appearing in my console, what does it mean and how do I fix it?  NullReferenceException: Object reference not set to an instance of an object How can I prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$  I have tried substitute $x,y$ for numbers, which turns out right, but I don't know how to reason here.  Thanks in advance! Here in the Figure R5=50K. This resistor value is not in the equations to obtain output voltage, and in many tutorials non-inverting input is directly grounded without a resistor. What might be the reason to use it here? How to install multiple versions of the same software? I manage phone systems for multiple clients. Each system uses the same administrator software, but it runs on different versions depending on what version of firmware is installed on the system controller.   The software is downloaded directly from the system controller so it's the right version. For example, if the controller runs on version 5.0.2, you have to run version 5.0.2 of the administrator software. You can't administrate a 5.0.2 controller with a later versions of administrator software.   Bottom line, you have to have the right version of software to log into the controller. The software is not executable on its own, you have to install it. So every time I want to log into a different controller, I have to reinstall the right software.   Any way to get around this?   I'm running Windows 7 Enterprise x86. Can you find shadow orbs in terraria demo? I have the PS vita demo, and was wondering if you could find any shadow orbs in that tutorial world. Thanks. A malevolent computer with AI takes over a woman's house with the intent of hybrid computer/human procreation. The evil computer seals off the house with the woman in it and keeps her prisoner while it prepares. I read the tale sometime in the late 80's or the early 90's. It was one of many of my missing books that got yardsaled by my in-laws when I wasn't looking. It may also have been made into a movie, but I didn't see the film. Capture characters from standard input without waiting for enter to be pressed I can never remember how I do this because it comes up so infrequently for me. But in C or C++, what is the best way to read a character from standard input without waiting for a newline (press enter).  Also ideally it wouldn't echo the input character to the screen. I just want to capture keystrokes with out effecting the console screen. Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$ NOTE: This is a Master Canonical Post for the issues observed on February 25, 2020.  All issues on Feb 25 relating to Python updates not found should be dupe-linked here.  Errors have been seen such as this today, February 25, 2021: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/p/python2.7/libpython2.7-minimal_2.7.17-1~18.04ubuntu1.3_amd64.deb 404 Not Found  Is there something up with the repositories?