This is NOT a duplicate question and I don't know why it is marked as one. This is a follow-up to a previous question asked here...  It seems that if (as per ZFC) we define sets as never containing themselves Russell's paradox goes away. Do other problems arise? (The system tells me this has been answered, but I beg to differ) EDIT: Perhaps I'm asking whether there is ever a need to define sets as being able to contain themselves, and if so what is the reason.
In ZF set theory the axiom of regularity (also called axiom of foundation) says that:     In all nonempty sets x there is an element y such that x∩y=∅   As I been told that  of the axiom is to prohibit constructions as $x\in x$, but is this a possible strategy?  Given a binary predicate $R$, written in infix notation, there are unitary predicates $p$ such that:  $\qquad \exists y \forall x: x R y \leftrightarrow p(x)$.  But there also are some convincing counterexamples:   $  p(x) \leftrightarrow \neg(x R x)$ $  p(x) \leftrightarrow \neg(x R f(x))$, where $f$ is any surjection $  p(x) \leftrightarrow$ all chains $x_1 R x, \: x_2 R x_1, \: x_3 R x_2,  \ldots \:$ are finite.   I think there is a major mistake to try to avoid certain paradoxical loops. First, there are no guarantees that every possibility is prohibited. And second, it seems pathological to make constructions that avoid certain proof-techniques (it's like the attitude of a shyster).  So, what protection comes from this axiom? Historically, has it anything to do with the Russell-predicate $x\notin x$?  See also
I co signed on a bank loan to finance the purchase of a car for my brother in Florida.  Only his name is on title, registration and insurance policy. Would I be liable and can I be sued by another person if he were in an accident? How to Toggle Selected Objects Visibility with H shortcut as in Maya There is something strange going on with Books on iPad and iPhone. It keeps deleting some books locally, keeping them in the cloud.  It's frustrating because it happens when I'm offline and I simply lose the access to them.  Why is this happening at all? And how can I stop it?  I enabled syncing things over iCloud Drive and everything, but I can't see an option to disable such optimizations.    PS: the same thing happens with Photos, Numbers and Pages. The Photos app has an optimize storage option. But there doesn’t seem to be such an option for Books, Numbers and Pages.   A clear example: just a few hours I was reading a book on Books, I took a nap, and when I opened the Books app, the book was not available offline anymore. Since I don’t have internet right now, it’s simply impossible to access the document. Visiting two Schengen countries, coming back home in between, do I apply for single-entry or multiple-entry visa? Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices? Let $\mathcal E=\{A \in \mathcal M_n(\mathbb R): A \text{ is of companion form} \}$. That is, $A$ has the following form \begin{align*} A=\begin{pmatrix}  0 &amp; \cdots &amp; 0&amp; -a_{0} \\  1 &amp; \cdots &amp; 0 &amp; -a_{1}\\ \vdots &amp;\ddots &amp; \vdots &amp;\vdots \\ 0 &amp;\cdots &amp; 1 &amp; -a_{n-1} \end{pmatrix}. \end{align*} Let $\mathcal D = \{A \in \mathcal M_n(\mathbb R): A \text{ is diagonalizable in $\mathcal M_n(\mathbb C)$}\}$. We know $\mathcal D$ is dense in $\mathcal M_n(\mathbb R)$. I am wondering whether $\mathcal E \cap \mathcal D$ is dense in $\mathcal E$. The set $\mathcal E$ is closed. It is not clear to me whether this statement is true. Is there a method to split thousands of polylines by employing a tool like the "Editor" - "Split" method and using distance, in ArcGIS?      When I utilize the "split" - "distance" tool (fig1), it only splits one section leaving the remainder unsplit (fig2).    I have attempted the "COGO" tool - using "Proportion", and can utilize the "duplicate" button to assign the remainder of segments which seems like a viable option.  But I would like to find some way to automate this process.  Has anyone found a method to do this?  Or is Python (coding) the only way?  I am trying to split over 2000 lines into equal distance segments (fig 3) of ~600m. Each segment will have its angle measured, and will ultimately result in a rose diagram representing angular statistics.  The distance of each segment is important in my splitting regime (a long line will have a greater representation of a particular angle on my rose diagram than the neighboring shorter line segments).  I currently am using ArcGIS 10.2 with an advanced user license. I think I accidentally pressed something to make it like this:    See how the XYZ arrows are at the 3D cursor instead of those vertexes I've selected?  How do I fix that? Whenever I select on a vertex or something, those blue, red, green arrows would always be where I selected, now it just keeps going to the 3D cursor. Extract information from a text file If I were to attack with a 4/4 indestructible creature and it's blocked by a 4/2 creature with first strike, would my indestructible creature still attack during the second combat damage step, or would it just tap, not assigning any damage? We all know some curves can be described by $y=f(x)$ and some surfaces can be described by $z=f(x,y)$ However, there exists curves and surfaces which cannot be described by those, such as a circle and a sphere. Therefore, we introduce parameterized vector equations, which can describe them. For example, circle: $\vec r(t)=r\cos(t)\hat i+r\sin(t)\hat j$ sphere: $\vec r(u,v)=\rho\cos(u)\sin(v)\hat i+\rho\sin(u)\sin(v)\hat j+\rho\cos(v)\hat k$ However, all curves described by $y=f(x)$ and  $z=f(x,y)$ can be parameterized. For curves, $$\vec r(t)=t\hat i+f(t)\hat j$$ For surfaces, $$\vec r(u,v)=u\hat i+v\hat j+f(u,v)\hat k$$ Therefore, I think this suggests the set of all parameterized surfaces (or curves) is the super-set of the set of all surfaces (or curves) described by $z=f(x,y)$ (or $y=f(x)$). Is that correct? Now, here comes the the real challenge. A curve can also be described by an implicit function $f(x,y)=0$ and a surface can also be described by an implicit function $f(x,y,z)=0$ I have 3 questions regarding this.   Can all surfaces (curves) described by an implicit function be parameterized? (If yes, then what is the general way?) Can all surfaces (curves) described by parametric vector equations be represented using implicit function? (If yes, then what is the general way?) Compare the set of all parameterized surfaces (curves) and the set of all surfaces (curves) represented by implicit function. (which is which super-set?)   Sorry for the use of nontechnical terms. I use them because I don't know the technical ones. I have only started learning vector calculus last year in university.  EDIT: I think my question is not too clear, so I will give an example of writing the surface $f(x,y,z)=0$ into $\vec r(u,v)$ We want to parameterize a sphere. $$x^2+y^2+z^2-\rho^2=0$$ Let $x=\rho\cos(u)\sin(v)$, $y=\rho\sin(u)\sin(v)$, $z=\rho\cos(v)$, $$\rho^2\cos^2(u)\sin^2(v)+\rho^2\sin^2(u)\sin^2(v)+\rho^2\cos^2(v)-\rho^2$$ $$=\rho^2\sin^2(v)(\cos^2(u)+\sin^2(u))+\rho^2\cos^2(v)-\rho^2=\rho^2-\rho^2=0$$ I want to know if there is a general way of finding $x=x(u,v)$, $y=y(u,v)$ and $z=z(u,v)$ for any given $f(x,y,z)=0$ Mask and inherit the same systemd unit Suppose a package provides whatever.service file so certain events (including whatever.socket) cause a daemon to start with a certain configuration.  I want to disable this completely. In particular, I want the old socket and any other unit files that might refer to this service by name to be unable to start the daemon.  Instead, I want to create my own unit files for this daemon with a different .socket unit and different environment variables. I also want my override to automatically take account of possible upstream updates to the original unit file (which my current solution of copying whatever.service as whatever-modified.service and editing it unfortunately does not provide).  If I create the following symlinks and files: /etc/systemd/system/whatever.service → /dev/null /etc/systemd/system/whatever-modified.service → /usr/lib/systemd/system/whatever.service /etc/systemd/system/whatever-modified.service.d/fix.conf  systemd considers the new service to be masked as well and refuses to start it. How to avoid this? I am using QGIS 3.2.0 on a Mac (and also have QGIS 2), and I have a fishnet grid (probably created in Arc) that comprises of nearly 2 million grid cells. As a result, every change I make to the attribute table takes hours, so I can't experiment as I would usually.  I need to label each grid cell such that the north-westernmost cell is "1", and the numbers proceed by rows, until the last number goes into the south-easternmost cell. Using the row-number doesn't work, as that's not how the table is sorted. I've done this before, but cannot remember how. How to find the inverse modulo $m$? Can I use an inner tube that's too narrow for the tyre? I recently got a puncture and when I went to replace the inner tube I discovered that I'd bought the wrong size tube. My tyre is 700 x 40c, the tube is 700 x 28-35c.  What is likely to happen if I use this tube? Will the tube explode when I attempt to inflate it? iCloud says Password is Wrong Even Though I Know It's Right iCloud says that my password is wrong - even though I know it's right.  Here's whats happened: Yesterday, I reset my iCloud password. Got the reset email, changed password. Tried to log in to the account, didn't accept it. I thought that maybe my finger had slipped typing in the password (twice). I called support, got the reset email.  Now, here's the really, really weird thing: I wanted to make sure I got the password right - so I typed my password into TextEdit, copied it into the reset fields and reset the password. After reseting it, I immediately went to icloud.com and tried to log in using the copied password from TextEdit. The passwords are the same. iCloud won't let me in. 3D bodies in TikZ Is there like a library that has default geometric figures like the ones shown below. Am not acquainted yet with 3D diagrams in TikZ. Which is correct: "This is her" or "This is she"? Upon answering the telephone, the person calling asks if Joan is available. If Joan is the person who answered the phone, should she say "This is her" or "This is she"? Callout Mock Responses & multiple HTTP Status Code values I'm trying to unit test the behavior of some code which performs callouts and its logic is dependent on the HTTP status code of the response - 200 vs 401.  The pattern being exercised is familiar:   Make callout Response is (unauthorized) HTTP 401 Logic checks Status value on the response if (status == 200) { /* yay! */ } if (status == 401) { /* make request for auth /* }   retry original callout with newly acquired authorization yay!    I am attempting to test the code's "try, auth, retry" behavior using the MultiStaticResourceCalloutMock but it appears that only a single status code can be set for all requests that the mock provider can respond to using the .setStatusCode(int) method. Is this accurate?  Is there a mechanism for using a single MultiStaticResourceCalloutMock and having it respond with different status codes per URL in the test context?  Is the only solution here to use a Dispatcher such as what Andrew Fawcett documents here in this answer?   Is there another method/mechanism that allows for different status codes to be returned by the mock provider on the HTTPResponse?    Some  showing the one-time usage pattern of the .setStatusCode(200) method and the multimock class.  @isTest private class CalloutMultiStaticClassTest {     @isTest static void testCalloutWithMultipleStaticResources() {         // Use MultiStaticResourceCalloutMock to         // specify fake response for a certain endpoint and          // include response body in a static resource.             MultiStaticResourceCalloutMock multimock = new MultiStaticResourceCalloutMock();         multimock.setStaticResource(             'http://api.salesforce.com/foo/bar', 'mockResponse');         multimock.setStaticResource(             'http://api.salesforce.com/foo/sfdc', 'mockResponse2');         multimock.setStatusCode(200);         multimock.setHeader('Content-Type', 'application/json');          // Set the mock callout mode         Test.setMock(HttpCalloutMock.class, multimock);          // Call the method for the first endpoint         HTTPResponse res = CalloutMultiStaticClass.getInfoFromExternalService(             'http://api.salesforce.com/foo/bar');         // Verify response received          System.assertEquals('{"hah":"fooled you"}', res.getBody());          // Call the method for the second endpoint         HTTPResponse res2 = CalloutMultiStaticClass.getInfoFromExternalService(             'http://api.salesforce.com/foo/sfdc');         // Verify response received          System.assertEquals('{"hah":"fooled you twice"}', res2.getBody());     } } How can I add a "C" wire to my thermostat? So, the spiffy new wi-fi thermostats want power on the C wire from thermostat, but the old thermostat doesn't have a C wire at it.  What's the easiest way to add the C wire/24 volt to the thermostat location? Dual citizenship passports and visas This is about entering the USA. I have   Hungarian citizenship with a 10 year B1/B2 visa in my passport I got before Hungary became part of the VWP. Real soon now, I will become a Canadian citizen (my oath is on April 5th) and will get a passport.   Since I, as a person, have a visa, am I obliged to enter into the USA with that? Or can I just forget it and use my Canadian passport? I know I could do whatever I want if I didn't have a visa but with that in the picture I am unsure.  describes a number of situations but not mine.