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Difference between live and neutral wires In domestic electrical circuits, there are 3 wires - live, earth and neutral. What is the difference between the live and neutral wires?  As there is AC supply, it means that there are no fixed positive and negative terminals. Current rapidly switches direction. Does that not mean that both the live and neutral wires carry the same amount of current, alternatively? Why is the neutral wire called 'neutral'? Security Review - CRUD/FLS Checks for every SOQL Query I know this sounds like a standard question, so please bear with me.  Recently our Security Reviews fail due to CRUD/FLS violations. The highlighted codelines include almost every SOQL Query in the application.  Our approach is usually as follows:   In case of displaying data on VF pages we either use sObjects fields or use the platform methods to check the accessibility of the fields In case of domain logic triggered by the user (e.g. by clicking a button on a VF page) we have a helper class that checks every field to be updated before doing the DML operation.   Up until recently this approach has worked fine (and passed pervious Security Reviews). As mentioned above the latest Security Review results seem to require us to check every field in a SOQL query for accessibility even if it is never displayed back to the user.    Let's suppose the following program flow as an example:   Query an object with some fields Perform some modification on said fields Perform an update on the sObject to save the modification using a helper class which checks for the required CUD/FLS rights for the modified fields   As I see it there is no need for checking field accessibility in step 1 in that case (since nothing is displayed back to the user and the dml operation is already protected). Is that correct or am I missing something? So is it really required to do an accessibility check for every SOQL Query in the code?  Another question would be how to handle background operations in that case like data purging. These have either to be running in system mode (which causes issues during the Security Review) or require the job to be started by a user with the appropriate access rights (which can be error prone and is not that user friendly). Is there any best practice regarding that.  Unfortunately I could not find a question targeting exactly that issue. Most of the questions I have found are related to how to perform that check (like  or ). So please apologize in case the question was already answered (I would really appreciate a link to the answer then).    Thanks for your time and help.  Mathias If the dual spaces are isometrically isomorphic are the spaces isomorphic? How to produce a longer \sim with a small letter on top Find $f$ if $$ f(x)+f\left(\frac{1}{1-x}\right)=x $$ I think, that I have to find x that $f(x) = f\left(\frac{1}{1-x}\right)$ I've tried to put x which make $x = \frac{1}{1 - x}$, but this equation has no roots in real numbers. Who's at fault with this error concerning csquotes and LuaLaTeX? I ran into this with the package lilyglyphs but I'm not sure whose fault this error is.  When I compile the following with lualatex:  \documentclass{article} \usepackage{csquotes} \MakeOuterQuote{"} \EnableQuotes \begin{document} \directlua{print("hello")} \end{document}   I get an error saying   \directlua]:1: unexpected symbol near '\'. l.6 \directlua{print("hello")}    Now suppose that I do not directly write \directlua in my document, but I include a package that does it internally. Such as   \documentclass{article} \usepackage{fontspec, csquotes, lilyglyphs} \MakeOuterQuote{"} \EnableQuotes \begin{document} \wholeNote \end{document}   I have no knowledge why compilation fails, because the error now becomes   ! Missing number, treated as zero. &lt;to be read again&gt; \begingroup l.7 \end       {document}    From my user point of view I did nothing wrong, because I'm using the public API provided by the packages. The csquotes documentation specifically says:     Note that all characters are automatically checked for validity as they are allocated. This package will reject characters which are unsuitable as active quotes... In sum, the following   characters will be considered as reserved by this package:   A–Z a–z 0–9 . , ; : ! ? ' - # $ % &amp; ^ _ ` ~ \ @ * { } [ ]    So my question is whose fault is this error?   My fault, the user's fault, because I should have known (but how?) that even though the quote is not listed as unsuitable in the csquotes manual, it actually is? The fault of the implementation or documentation of csquotes for failing to mention " as unsuitable? The fault of the implementation of the \directlua command because it doesn't prevent LaTeX catcode changes/active characters from impacting its argument? A shortcoming of TeX itself because of its global state based architecture? A question about the arctangent addition formula. In the arctangent formula, we have that:  $$\arctan{u}+\arctan{v}=\arctan\left(\frac{u+v}{1-uv}\right)$$  however, only for $uv&lt;1$. My question is: where does this condition come from? The situation is obvious for $uv=1$, but why the inequality?  One of the possibilities I considered was as following: the arctangent addition formula is derived from the formula:  $$\tan\left(\alpha+\beta\right)=\frac{\tan{\alpha}+\tan{\beta}}{1-\tan{\alpha}\tan{\beta}}.$$  Hence, if we put $u=\tan{\alpha}$ and $v=\tan{\beta}$ (which we do in order to obtain the arctangent addition formula from the one above), the condition that $uv&lt;1$ would mean $\tan\alpha\tan\beta&lt;1$, which, in turn, would imply (thought I am NOT sure about this), that $-\pi/2&lt;\alpha+\beta&lt;\pi/2$, i.e. that we have to stay in the same period of tangent.  However, even if the above were true, I still do not see why we have to stay in the same period of tangent for the formula for $\tan(\alpha+\beta)$ to hold. I would be thankful for a thorough explanation. I have a Google Apps email (me@business.com) set to auto-forward all mail to my personal Gmail (me@gmail.com).  I have added the me@business.com address to my personal Gmail so I can send mail as me@business.com from within my personal email account.  It's a fairly common way to consolidate email accounts.  Here's my problem.  I want me@gmail.com to filter all emails being forwarded from me@business.com and apply the Business label.  So I tried it two different ways:  A) Use an Alias:   me@business.com forward to me+business@gmail.com Create filter "To:me+business@gmail.com" in me@gmail account Have filter apply Business label   B) Use Googlemail.com address:   me@business.com forward to me@googlemail.com Create filter "To:me@googlemail.com" in me@gmail account Have filter apply Business label   However, neither of these filters work.  I've tested it using a third email address, me@yahoo.com.  Whenever I send an email from me@yahoo.com to me@business.com, the email is properly forwarded to me@gmail.com, and I can reply to me@yahoo.com using the me@business.com address.  But Gmail does NOT apply the Business label.  This is case using either filtering method A or B.  But if I send an email from me@yahoo.com DIRECTLY to me+business@gmail.com or me@googlemail.com, the filter works properly and applies the label.  So there must be something going on with the forwarding of me@business.com to me@gmail.com.  Does anyone know how to get this working? How did Luke know where to land on Dagobah? What do the different colors mean in ls? Proof a $(2n-1)$-compact manifold I have no idea how prove that $$\{(z_0,\ldots,z_n)\in\mathbb{C}^{n+1} \quad| \quad z_0^d+z_1^2\ldots+z_n^2=0, \quad |z_0|^2+|z_1|^2\ldots+|z_n|^2=2\}$$ is a $(2n-1)$-compact manifold.  How give the charts. For $n=1$ and $d=2$ not distinguish which 1- manifdold is? Classify all groups with order $pq$, $p$ is not equal to $q$ I am reading the following material:  . At page 5, there is a proof classifying all groups with order $pq$(they are all primes and $p$ is not equal to $q$). I am lost in the last two sentence, which claims the semidirect product are all isomorphic. Could someone help me to understand it? Thanks! How to divide aleph numbers Digonalizable Polynomial Matrix For any polynomial $p(x) = a_0 + a_1x + · · · + a^kx^k$ and any square matrix A, $p(A)$ is defined as $p(A) = a_0I + a_1A + · · · + a_kA^k$. Show that if v is any eigenvector of A and $χ_A(x)$ is the characteristic polynomial of A, then $χ_A(A)v = 0$, Deduce that if A is diagonalizable then $χ_A(A)$ is the zero matrix.  I got that $p(\lambda)$ is the eigenvalue of $p(A)$ and if A is diagonalizable then $χ_A(x)$ is the zero matrix since p(A) is similar to its diagonal matrix p(D)  $$p(D) = a_nD_n + · · · + a_1D + a_0I$$  =  $\begin{matrix} p(\lambda_1) &amp;0&amp;...&amp;0\\0&amp; p(\lambda_2)&amp;...&amp; 0 \\ ...&amp;...&amp;...&amp;...\\0&amp;0&amp;... &amp; p(\lambda_n) \end{matrix}$ Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$ I have a question that I need help with getting started (possibly I would be back for more help).     I have a measure space $(X,A,\mu)$ that is finite, and $f \in L^{\infty}(\mu)$. Also, defined is $a_n = \int_X\,|f|^n\,d\mu$. I need to show that the limit is: $$\lim_{n\to\infty}\,\frac{a_{n+1}}{a_n} = \|f\|_{\infty} .$$   I am stuck on getting started, anybody have any suggestions?  thanks much Every planar graph has a vertex of degree at most 5. Dynamic Object Intellisense Can Mjolnir "stick" to anything? How do you get the logical xor of two variables in Python? Difference between 2>&-, 2>/dev/null, |&, &>/dev/null and >/dev/null 2>&1