John von Neumann- Exercise about a Fly and two Trains
Fly and Two Trains Riddle
SQL JOIN - WHERE clause vs. ON clause GIS Point or discrete longitude and latitude columns? I see that the Point type is made to store geometric coordinates, however I don't see what problem it is trying to solve, or what advantages it offers over simply using two numerical columns. It's 16 bytes, so is it just an abstraction for two 8 byte floats? Or is it a string containing some kind of geohash that optimizes the performance of certain queries?  Let's say I want to get all the points for a specific viewport on a Leaflet map... with numerical columns representing latitude and longitude, I'd just filter for all the rows that have a latitude number between the N/S bounds and a longitude number between the E/W bounds, easy. I looked into using Point here, but the syntax is cumbersome and it seems to me like unnecessary overhead for development and for database performance... is it? Align  elements side by side I don't understand this and I'm now worried as I have donated to a lot of servers and I don't want to lose this account. On the launcher it says my new username but when I log on it says "Account not Authenticated with minecraft.net" and "Non-Valid Username".  How can I regain the ability to use my account online? Do Cleric's domain spells add slots? I'm a little bit confused with the whole spell system and additions to them. If I pick for instance Tempest Domain Spell, are the spells additional to the other ones? (2 at level 1) So do that make it 3 spells? Does the domain add slots too?  And also, I've read about people choosing multiple domains, is that possible? Interaction of Invoke Duplicity and Misty Step Search for ,        ,                        and you will see that "results found containing __" is just a little too close to the header. It's not like there isn't  to have it be a little lower, closer to "Search":          The UI has been updated since I took the above screenshots, and the text you search for is  (which fixes another design issue but not the one in this question): Probability of student passing an exam There're $25$ tests, each with $2$ questions. There're total of $50$ different questions (the questions do not repeat). The student knows the answer of $44$ questions. To pass the exam, the student needs to correctly answer both questions on the first test he drew, or answer $1$ question from the test he drew first, and $1$ question from the test he drew second. (meaning he draws twice if he answers a question incorrectly on his first try)  What is the probability that the student will pass the exam?  I have never faced a problem like this one so any help is appreciated. I was thinking about approaching it "manually" with some applied combinatorics but I feel like there's a much easier way that I am not familiar with. Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository ... doesn't support architecture 'i386' I installed Ubuntu 18.04 and then while installing Virtualbox i get the 'i386' error message after I did:  $ sudo apt-get update Get:1 http://nl.archive.ubuntu.com/ubuntu bionic InRelease [242 kB] Hit:2 http://security.ubuntu.com/ubuntu bionic-security InRelease                                                                 Hit:3 http://ppa.launchpad.net/danielrichter2007/grub-customizer/ubuntu bionic InRelease                                          Hit:4 http://nl.archive.ubuntu.com/ubuntu bionic-updates InRelease Hit:5 http://nl.archive.ubuntu.com/ubuntu bionic-backports InRelease Get:6 http://download.virtualbox.org/virtualbox/debian bionic InRelease [4429 B] Get:7 http://download.virtualbox.org/virtualbox/debian bionic/contrib amd64 Packages [1426 B] Fetched 248 kB in 1s (209 kB/s)      Reading package lists... Done N: Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian bionic InRelease' doesn't support architecture 'i386'   I found several answers on Askubuntu for the 'i386' message but I don't know how to apply this to my situation Is there a way to offset an edge? (extrude edge loop perpendicular to each edge) I recently figured out how to do it with faces, but with edges, I can't seem to get it to work. I have a complex flat plane and i need to extend an edge loop. I tried setting to individual origins in combination with all possibilities for x,y,z axes in global and local, but it is still not extruding along the normals.   actual problem   simplified Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... Getting tabular statistics from table using QGIS? Are there QGIS tools that will allow users to get tabular statistics from their table?  I kind of expected I would be able to just open the table, select the field I was interested in, right-click on the field header and get something similar to this (screenshot taken from ArcGIS):    More specifically, I am looking for a QGIS alternative to the ArcGIS  and  tools, that offer a  you can retrieve about the tabular data.    Just after asking, I found  (see section 4.2 ) that describes how to find this functionality... Vector > Analysis Tools > Basic statistics.  I also found Vector > Analysis Tools > List Unique Values right next to it.  This gets me the list of unique values, but I would also like to see an additional column of frequency (count) of each unique item.  Is this similar tool available "out-of-the-box"? I want to create this:  Note that wire lay chaotically, so spiral object not the same thing.  There is a cool way to do this task in 3ds max:  Basically he deform straight spline/curve and then bend it couple iterations (over 9000 degrees angle in max).   Blender can't bend that way with simple deform as I know, only up to 360 degree. Is there any other way to make wire wrapping similar to photo? How can an encryption scheme be indistinguishable with multiple messages but vulnerable to an adaptive chosen-plaintext attack? In order to be indistinguishable with respect to multiple messages, wouldn't the scheme need to be nondeterministic? How would this then possibly be vulnerable to an adaptive CPA? How to get this blur texture effect in photoshop? How to prevent applications from discovering my phone as being Rooted I have to install an application that has discovered my device to be rooted.  So this is a two part question.   How did it discover in the first place that my phone has been rooted How to prevent the application from discovering my phone as being rooted Error message on Terminal launch Can newsletters take into account a user's favorite tags on that site? In Ubuntu 18.04.1, I would like to use my left Super-key only to simply open the Show Applications menu (aka Dash) like a left click on the dock-icon (with the 9 dots) does and preferably close it again without showing me any open programs.   I can open it with Super + A and even close it again with Super R, but Super L appears to do nothing at all.   In Xfce, something similar was possible by adding a custom keyboard shortcut for Super L and setting the command to xfce4-popup-whiskermenu, which would open and close a menu with favourite applications. Unfortunately, I don't know the command that opens and closes the Show Applications menu.   Is there any way to add such a shortcut in the new Gnome Shell? What is the difference between 'git pull' and 'git fetch'? What are the differences between git pull and git fetch?