It is well known that $\oplus$ produces a plus sign with a circle around it, similarly $\otimes$ does the and same with the $\times$ symbol, etc.  I was wondering if there a way to make a command which would do the same for $\div$ ?   The command isn't available by default, to my knowledge, and I'm not experienced enough with defining such commands myself.
I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
How to request a random row in SQL? We are conducting a test on a rare disease. A positive result means that, according to the test, the subject is infected. The following characteristics are known about the test and the disease: If a person is infected, the person has a $95\%$ chance of testing positive. When a healthy person is tested, the test has a $99\%$ chance of giving a negative result. A mere $0.1\%$ of the population is infected with the disease. If a person is tested positive for the disease. What is the probability that the person actually has the disease? I don't understand how to write the conditional probabilities if someone can explain to me than I should know how to solve it, but I'm not sure how to convert the text into the mathematics language. In course of evolution (possibly), mammary glands became vestigial in male mammals, but became fully developed in females. Is there any plausible explanation for this characteristic? Why are we in love "with" someone? Class imbalance in Supervised Machine Learning How to Deserialize XML document Why the statement "there exist at least one bound state for negative/attractive potential" doesn't hold for 3D case? Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal.   However, today I'm doing a homework considering a potential like this:$$V(r)=-V_0\quad(r&lt;a)$$$$ V(r)=0\quad(r&gt;a)$$ and found that there is no bound state when $V_0a^2&lt;\pi^2\hbar^2/8m$.  So what's the condition that we have at least one bound state for 3D and 2D? Precedence of user and group owner in file permissions I just ran into something unexpected (for me) regarding file permissions on Linux (Arch Linux). Basically I have:   userX in groupX fileX userX:groupX ---rwx----   What puzzles me: I cannot perform any action (rwx) on fileX. Is this right? Can someone please confirm this is indeed the expected behaviour?  The only actions I can perform are mv and rm because I have write permissions on the parent directory.  The thing is, I always thought these permissions collapse on each other, starting with the most general one (other -> group -> user). In other words, if o=rwx who cares what the persmissions for group and user are? Apparently this is not the case but it doesn't make much sense to me; it seems counterintuitive. The only thing this approach seems to be useful at, is to easily exclude a very specific person / group, which doesn't seem like a smart way to go at it (imho). Besides, the owner (and group?) should be able to chmod anyway right? Any thoughts on this matter? double movement in Scrabble Can you resolve a dispute between myself and my girlfriend? She recently won a game with what I think is a double movement (although there's no mention of this in the rule book).  She put one two letters down to make one word, which also scored linked to another letter. But she then added another letter immediately to the left of the finished word, which then extended the second word. I just don't think you can make a second movement like this in scrabble!    My sister placed down W, D and E, the ones that I circled in red. Is she allowed to do that? I told her it was impossible is it?  Can you resolve this for me please? Is there any general way to obtain the review ID or review summary for a certain review job without the 10 k tools? Accessing the full review history is a privilege for 10 k users but, statistics for individual reviews can be viewed by everybody ( ).  These review summaries can be somewhat useful for different aspects, such as understanding what happened to a review item that you initiated, e.g., if your close vote remained the only one on a question, you can only guess by the elapsed time whether nobody else has reviewed it or whether the review is finished with everybody disagreeing. Or you can see who performed a disputed review decision and discuss it.  My question now is: Is there any way to acess these review summaries or obtain the review ID – which would allow to find these summaries – for a particular review task?  I am aware that the above information, in particular the reviewer identity, can be abused and it may therefore be undesirable that everybody can find this information. But then, at least on small sites, it’s quite possible to obtain the review ID from guessing. Also, I can access the review summary for every review that I participated in or even skipped from my review history and the review summary for every successful edit from the edit history. Mean, Average and Expectation What is the precise difference between the Mean, Average and Expectation ? Is there any mathematical formaulation to show the difference ? I see that often they are used interchangeably. I've been using Windows 10 for a couple of month now (joined the Insider Preview).  Now my hard drive started ticking so I've bought a new SSD and I want to move the windows installation to the new hard drive, which has been connected to the computer (unpartitioned). I don't mind and I even prefer reinstalling it over again.   Since I have the free version of Windows 10 pro, can I still reinstall it anew? Does the windows 10 installation offer disk management and partition like the older Windows installations used to? How should I reinstall Winodws 10 x64 the easiest but still remain on free mode? How to pretty print XML from Java? I have a Java String that contains XML, with no line feeds or indentations. I would like to turn it into a String with nicely formatted XML. How do I do this?  String unformattedXml = "&lt;tag&gt;&lt;nested&gt;hello&lt;/nested&gt;&lt;/tag&gt;"; String formattedXml = new [UnknownClass]().format(unformattedXml);   Note: My input is a String. My output is a String.   (Basic) mock result:    &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;root&gt;   &lt;tag&gt;     &lt;nested&gt;hello&lt;/nested&gt;   &lt;/tag&gt; &lt;/root&gt; SQL - Stored Procedure with Select Statement using IN (@Variable_CommaDelimitedListOfIDS) I have two dates of the form:  Start Date: 2007-03-24  End Date: 2009-06-26   Now I need to find the difference between these two in the following form:  2 years, 3 months and 2 days   How can I do this in PHP? What is an "index out of range" exception, and how do I fix it? Proof that no polynomial with integer coefficients can only produce primes Doing a discrete math review and am trying to solve problem 1.6 in the text found here:  - I believe I've gotten parts (a) and (b) correctly, but (c) is a bit tricky for me. Would appreciate a review of a/b and a hint for c if possible. Restatement here:  For n = 40, the value of polynomial $p(n)::=n^2 + n + 41$ is not prime, as noted in Section 1.1. But we could have predicted based on general principles that no nonconstant polynomial can generate only prime numbers.  In particular, let $q(n)$ be a polynomial with integer coefﬁcients, and let $c::=q(0)$ be the constant term of q.  (a) Verify that $q(cm)$ is a multiple of c for all $m \in Z$  Proof: Since q is a polynomial, it will be of the form: $q(x) = a_nx^n+a_{n-1}x^{n-1} + ... + a_1x + c$  If $x = cm$, then notice that cm will be inside every term of the polynomial, and since the final term is c, c can be factored out of every term. Hence, q(cm) is a multiple of c for all $m \in Z$.  b) Show that if q is nonconstant and c > 1, then as n ranges over the nonnegative integers, $N$, there are infinitely many $q(n) \in Z$ that are not primes.  Proof: Continuing from the result found in (a), it is easy to see that for all $m \in Z$, there will be an infinite number of multiples of c that will be generated by q. Since c > 1, these multiples are guaranteed not to be prime.  c) Conclude that for every nonconstant polynomial, q, there must be an $n \in N$ such that $q(n)$ is not prime. Hint: Only one easy case remains.  c = 0 is trivially easy to prove using the (b) above.  I assume the "easy" case is referring to c = 1, but in this case I'm not sure how to continue, since the result of (a) and (b) don't apply: I can't use them since adding 1 to any even number may make it prime. If the result of the terms not including c is odd, then adding 1 to that result makes it even and it is not prime. However, if the terms add up to an even number, I don't see a way of using the knowledge I have so far to prove conclusively that that number + 1 will NOT in fact be prime. How to set up Dolphin as default file manager? Intuition behind the definition of a measurable set This week I saw the definition of a measurable set for an outer measure.     Let $\mu^*$ be an outer measure on a set $X$. We call $A \subseteq X$ measurable if $$\mu^*(E) = \mu^*(A\cap E) + \mu^*(A^c\cap E)$$ for every $E \subseteq X$.   This is not the first time I've seen this definition. Unlike most other things in mathematics, over time I have gained absolutely no intuition as to why this is the definition.   The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not comfortable with it is that you require a measurable set to break up sets which, according to this definition, are non-measurable; why would you require that? Of course, you can't say what a non-measurable set is without first defining what it means to be measurable so I suppose no matter what your condition is, it will have to apply to all subsets of $X$.     Is there an intuitive way to think about the definition of measurable sets? Is there a good reason why we should use this definition, aside from "it works"? Ubuntu 19.10 change desktop environment