Is this element a subset of set A?
Element of, subset of and empty sets
Why is James Bond less tech savvy in the Daniel Craig movies? The most recent installments of  (ones featuring Daniel Craig) have fewer gadgets but more raw action (like the chase sequences in Casino Royale and Quantum of Solace). Is it because of plot related changes to the MI:6 or have the movies been altered to suit the audiences? Idempotent of closure and other properties My refrigerator line is 20 amp with 12 gauge wire. Can I tap into that with 14/2 wire, and run a light switch and 1 LED light? Where can I find out when the next kernel version will be released for my distro version? I checked the , , and  wiki pages but still cannot seem to find a complete answer to this.  When using an LTS release like 18.04, is there somewhere public that can be checked to determine what kernel versions are being tested and when they are anticipated to be released for it? I would like to use 4.19, for example, but would like to know how to check this for any anticipated kernel release.  I know I could potentially just install the 4.19 kernel myself but I would rather know when it (and future kernel releases) were in the release pipeline. Is there somewhere on Launchpad that I could check? Somewhere else? Where are the Ubuntu kernel package maintainers doing their work? Recently I booked a flight using my points. I am  planning to fly to Seattle WA from Indianapolis Indiana.  Stop over is Chicago.  On the day of my flight I am supposed to be in Chicago.   So I was wondering if I can directly board my Seattle flight from Chicago thereby not showing up in Indianapolis.  Is this okay?  Will United airlines cancel my entire journey if I do not show up in Indianapolis? Is there a problem with Beamer in the latest MiKTeX update? This is about MiKTeX Revision 2.9.6360.  Immediately after the latest MiKTeX update, my Beamer files stopped compiling.  When i tried to compile a file that had been working fine I got a Package installation popup saying:  tex\latex\beamer\beamerbasemodes.sty  Is missing.  It is part of the following package  beamer   So i clicked to have it installed.  All that achieved is that i got an error message  ! LaTeX error: File 'beamerbasemodes.sty' not found   I repeated this a few times with minor changes to the file, and then went to the MiKTeX Package Manager to see what parts of Beamer are installed.  It said none were.  Either the update had removed Beamer, or the attempt to install beamerbasemodes on the fly had done it.  So I reinstalled it by hand.  In fact i did this several times in various ways.  It made one difference.  Sometimes the problem package was identified as  translator.sty  In case it would help, I ran Update FNDB and restarted my machine.  Each time I installed Beamer, the Package Manager then reported that Beamer was installed.    But when I tried to compile the file, the same things happened all over.   And when i went back to the MiKTeX Package Manager it reported Beamer is not installed.   Is Beamer now out of date?  Or is this a problem on the new update?  Is there a simple fix i can use? I must be missing something with regards to setting up PostgreSQL. What I'd like to do is create multiple databases and users that are isolated from each other so that a specific user only has access to the databases I specify. However, from what I can determine, any created user has access to all databases without any specific grants being given.  Here is what I do on an Ubuntu Server 12.04:   apt-get install postgresql sudo -u postgres createuser -DRSP mike1 (Specifying the password for the new user) sudo -u postgres createdb data1 psql -h localhost -U mike1 data1 (Specifying the password for the user mike1 to login)   It seems that new user "mike1" has no problem connecting to database "data1" and creating tables etc. And this without running any GRANT command at all (and the owner of "data1" is "postgres" since I didn't specify an owner in step 3). Is this really how it is supposed to work?  What I'd like to do is grant mike1 full access to data1 and then repeat this for more users and databases, making sure that the users only have access to one (or possibly several) databases of my choice. I need to calculate the SQRT of  $x$ to $y$ decimal places. I'm dealing with $128$-bit precision, giving a limit of $28$ decimal places. Obviously, if $\,y &gt; 28$, the , which I'm currently using, becomes futile, as it simply doesn't offer $y$ decimal places.  My question to you is, can I calculate the Square Root digit-by-digit? For example, calculating the $n$-th digit, assuming I already have digit $\,n - 1$. I'm well aware this may be impossible, as I've not found any such method through Google yet, just checking here before I give up in search of arbitrary precision methods. I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other? What is the most popular open source password manager which I can use on a Ubuntu machine or preferably across Ubuntu/Windows machines with some form of data compatibility. If there is a free web based version, that would be even more preferable. Remove specific duplicates (all but latest) When removing duplicate rows, using the below query from  tutorial, how would I go about forcing which of the found duplicates to remove?  DELETE FROM dbo.ATTENDANCE      WHERE AUTOID NOT IN (SELECT MIN(AUTOID) _ FROM dbo.ATTENDANCE      GROUP BY EMPLOYEE_ID,ATTENDANCE_DATE)    And this works great. The reason why I am using this one is because the only unique id available is one in the IDENTITY column. And to determine if there are duplicate rows I have to look at a combination of multiple columns.    But if I have a set of duplicate rows how do I / how does SQL Server decide which to remove? And how would I force it to remove all but the one with the highest IDENTITY value?  EMPLOYEE_ID     ATTENDANCE_DATE     AUTOID A001            2011-01-01          1 A001            2011-01-01          2   If I would run the query now it happens to remove the second one, with AUTOID 2. But I am trying to remove all but this one (because this is the one latest added). Homework question on whether two quotient spaces are homeomorphic How do you deserialize json properties that are reserved words in apex? Is there any way to deserialize JSON into an object using JSON.deserialize if some of the property names in the JSON are reserved words in apex? I want to do something like this:  string jsonString = '{"currency" : "ABC"}'; public class JSONResult {     public string currency; } JSONResult res = (JSONResult) JSON.deserialize(jsonString, JSONResult.class); system.debug(res);   but of course I get an error that the identifier name is reserved. Can a sum of a finite number of square roots of integers be an integer? If yes can a sum of two square roots of integers be an integer?  The square roots need to be irrational. How do I create an 8 sided die from one object? Simply put, is there a way to make a cube balance solely on one point/vertex?  I'm struggling. I do not want to have to join two objects, nor have to extrude an object. I just want to have a simple eight-sided die created with one mesh. Every ordered field has a subfield isomorphic to $\mathbb Q$? I'm going through the first chapter in a text on real analysis, which contains preliminaries on ordered fields, the real numbers, etc. Supposedly I had learned about such things already, in calculus, but I thought it wouldn't hurt to go over it again.  Up until the paragraph which is the subject of my question, everything is thoroughly proven and examples are provided. However the following excerpt just goes through facts, whose proof I cannot conceive:      Although $\mathbb Q$ is an archimedean field, these properties cannot be used to define $\mathbb Q$ since $\\$ there are many Archimedean ordered fields. What distinguishes $\mathbb Q$ from the other $\\$Archimedean ordered fields is that $(\mathbb Q,&lt;)$ is the $smallest$ ordered field in the following sense: $\\$ if $(X,\prec)$ is an ordered field, then $X$ contains a sub-field which is (field) isomorphic to $\mathbb Q$.$\\$ Furthermore such an isomorphism preserves the order relation.   I've concatenated the paragraph a bit, so the text isn't idem from the book (if anyone wishes to know it's Phillips, An Introduction to Analysis and Integration Theory, Dover Publications). Also $\mathbb Q$ contains no proper subfields, and this can be verified by the apparently easy-to-prove fact that, if a field has characteristic zero, then it contains a subfield isomorphic to $\mathbb Q$. Then it remains to prove the preservation of order.  I'm guessing that some concepts from abstract algebra or field theory would easily suffice, but at the moment such topics are a bit over my head, so all I can think of doing is actually constructing the isomorphism $\phi:\mathbb Q\to\hat{\mathbb Q}$, where $\hat{\mathbb Q}$ is a certain subfield of  $X$ in such a way that field operations are preserved, but I really can't come up with anything. So the question is: how do I construct this isomorphism, or, if there's a better way of proving this, how is it done? Thanks for any help.  Edit: Assume the existence of $(\mathbb Q,&lt;)$ as an archimedean ordered field. How to draw arrows between circled coefficients of polynomials using tikz Is there a way I can avoid imperial ships? Whenever I am traveling on foot, imperial ships will fly by and drop down troops for me to fight. In a normal situation, this is no big deal and I will fight or flee to continue with my travels.  However this will also occur when I am doing a quest that requires me to locate and pick up items. This is an inconvenience as I cannot pick up items while in combat and I have to kill them before I can continue.  Is there a way I can "hide" and allow the ships to by pass my location? Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$ Are "w/o", "w/", "b/c" common abbreviations in the US?