How to speak on limit of sequence categorically?
Category-theoretic limit related to topological limit?
Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$ It's a standard result that given $X_1,\cdots ,X_n $ random sample from $N(\mu,\sigma^2)$, the random variable $$\frac{(n-1)S^2}{\sigma^2}$$ has a chi-square distribution with $(n-1)$ degrees of freedom, where $$S^2=\frac{1}{n-1}\sum^{n}_{i=1}(X_i-\bar{X})^2.$$ I would like help in proving the above result. Thanks. Chrome: Site has updated in the background I keep getting these notifications despite not having an RT tab open. What gives? For some results returned in Google Search, on the right side it displays the company details, logo, contact numbers, etc...   For example, see the following screenshot:    I'd like to know what contributes to this so that I can try to achieve it for my site too. I tried running the following statement:  INSERT INTO VOUCHER (VOUCHER_NUMBER, BOOK_ID, DENOMINATION) SELECT (a.number, b.ID, b.DENOMINATION)  FROM temp_cheques a, BOOK b WHERE a.number BETWEEN b.START_NUMBER AND b.START_NUMBER+b.UNITS-1;   which, as I understand it, should insert into VOUCHER each record from temp_cheques with the ID and DENOMINATION fields corresponding to entries in the BOOK table (temp_cheques comes from a database backup, which I'm trying to recreate in a different format). However, when I run it, I get an error:  Error: Operand should contain 1 column(s) SQLState:  21000 ErrorCode: 1241   I'm running this in SQuirrel and have not had issues with any other queries. Is there something wrong with the syntax of my query?  EDIT:  The structure of BOOK is:  ID  int(11) START_NUMBER    int(11) UNITS   int(11) DENOMINATION    double(5,2)   The structure of temp_cheques is:  ID  int(11) number  varchar(20) Position of "only" in “We 𝒐𝒏𝒍𝒚 have two possibilities” Is there any difference in meaning between the three following sentences?   We only have two possibilities. We have only two possibilities. We have two possibilities only.   I have already read  and I know that the position of only and the emphasis (written or oral) may change the meaning of some sentences, but I am not sure if it does here.  Note: It is clear that “only we have two possibilities” has a different meaning. My question is restricted to the sentences I’ve listed above. Why does the definition of limits of a function have strict inequality? Definition (As written in Michael Spivak's Calculus)     The function $f$ approaches a limit $l$ near $a$ means: for every $\epsilon &gt;0$ there is some $\delta &gt; 0$ such that, for all $x$, if $0&lt;|x-a|&lt;\delta$, then $|f(x)-l|&lt;\epsilon$.   my question is: why can't it be: $$0&lt;|x-a|\leq \delta,|f(x)-l|\leq \epsilon$$ After looking at limits of functions for a long time just to grasp it's meaning and using the definition quite a lot solving homework I realized I keep writing the same inequality without really understanding why.  The only explanation given in Spivak's book for this part of the definition goes over it without explaining the inequality. I tried looking for an explanation myself but wasn't really able to find anything wrong with it. Is it also possible to write the definition like that or is there a problem with that?   (first non-homework related question :p) Should 'drive by' downvoting be more effectively caught? I have an answer that I'm certain is technically correct. However, it continues to be downvoted. The answer has already been noted in comments on other answers to be better. It goes more in-depth than the others, yet it continues to be downvoted.  The already upvoted answers were nowhere close initially, and I had already commented on them to say why it is wrong...  Isn't there a limit for that? Shouldn't something be catching this? Opacity of background-color, but not the text How do I make the cross-browser (including Internet Explorer 6) transparency for the background of a div while the text remains opaque?  I need to do it without using any library such as jQuery, etc. (But if you know of a library that does it I'd love to know so I can look at their code). MySQL convert date string to Unix timestamp I know that if you held an infrared remote in front of a digital camera, it'll flash a blue/purplish light when you press the buttons. Why?    (Image by  .) Scalar Field Theories The Lagrangian density for a single real scalar field theory is \begin{equation}\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-V(\phi)\end{equation} I have often seen this written \begin{equation}\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-V(\phi)\end{equation} which appears to differ in the kinetic term.  Specifically \begin{equation}(\partial_{\mu}\phi)^{2}=(\partial_{\mu}\phi)(\partial^{\mu}\phi)\neq\partial_{\mu}\phi\partial^{\mu}\phi=(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\phi\partial_{\mu}\partial^{\mu}\phi\end{equation} where the product rule has been used in the last equality. Is this just sloppy notation (which is acceptable because only first derivatives in the field are considered anyway), or is my maths very bad? I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. When I ssh into my Ubuntu 18.04 box I get the motd  1 update could not be installed automatically   Which goes on to tell me to check the unattended-upgrades log.  The log shows no problems. How can I clear this bogus message? I'm downloading GTA V. After 20gb / 100gb I paused my download for restarting my pc. Then download restarts from 0%.  Why this could happen? Can I restart my PC during downloads without losing progress? I need to create an edit component for an SObject from which I do not know the objectApiName at design time. I only know the Id of the SObject. objectApiName could be any valid SObject-name.  Now I want to use lightning:inputField   This needs to be wrapped by lightning:recordEditForm  In case I hardcode it to "Order", provide a vaild Order Id and let the controller load the order and assign it to the Parent-attribute, this works flawlessly:  &lt;aura:attribute name="recordId" type="String" default="" /&gt; &lt;aura:attribute name="Parent" type="SObject" default="{}" /&gt; &lt;aura:attribute name="ParentType" type="String" default="" /&gt; &lt;b&gt;{!v.ParentType}({!v.recordId})&lt;/b&gt; &lt;br/&gt; &lt;lightning:recordEditForm recordId="{!v.recordId}"  objectApiName="Order"&gt;     &lt;lightning:messages /&gt;     &lt;lightning:inputField fieldName="Name" /&gt;     &lt;lightning:button class="slds-m-top_small" variant="brand" type="submit" name="update" label="Update" /&gt; &lt;/lightning:recordEditForm&gt;   It looks like below and even the Update-button works as expected and saves the record:    But what I really want is  &lt;lightning:recordEditForm recordId="{!v.recordId}"  objectApiName="{!v.ParentType}"&gt;   Note the {!v.ParentType} instead of the hardcoded "Order"  As an great unfortunate, this only collapses to that error-popup    In the screenshot you see, that the ParentType is correctly bound to v.ParentType (right above the button) which a I also verify in the console  Suspicion  I set the ParentType-attribute as a result of APEX call (asynchronously). This seems to be too late for the lightning:recordEditForm. It tries to render with objectApiName at a time where it is still blank, hence it crashes during initialization...  Question  Is there a clean way to avoid this and get something to fly with an dynamic objectApiName?  Trying to use $A.createComponents()  As @sfdcfox suggested I jump on the $A.createComponents() which turned indeed out to be tricky, exactly as sfdcfox has predicted. Im following this .  Added a button to the markup    Added a handler to the js-controller:  makeEdit : function(cmp, evt, hlp) {      console.log('ParentId :: ', cmp.get("v.ParentId") );      console.log('ParentType :: ', cmp.get("v.ParentType") );      $A.createComponents([             ["lightning:recordEditForm",{                 "recordId"          : cmp.get("v.ParentId"),                 "objectApiName"     : cmp.get("v.ParentType"),             }],             ["lightning:inputField",{                 "fieldName" : "Name"             }]         ]         ,function(components, status, errorMessage){             if (status === "SUCCESS") {                 var wrapper         = components[0];                 var inner           = components[1];                 wrapper.set("v.body", inner);             }             else if (status === "INCOMPLETE") {                 console.log("No response from server or client is offline.")                 // Show offline error             }             else if (status === "ERROR") {                 console.log("Error: " + errorMessage);                 // Show error message             }         }     ); },   Now I can press the button - but nothing - I repeat: n o t h i n g - gets rendered at all. What is my fault here? Note that the console.log get output and the attribute are holding good values. How can I have colored and underlined links with hyperref? I would like the internal hyperlinks generated by  to be colored and underlined.    Reading some of the package documentation, I know that these \hypersetup keys exist:   colorlinks: when true, color the link; when false, draw a border around the link and color that. linkcolor: the color of the link (requires colorlinks=true to have any effect) linkbordercolor: the color of the link border color (requires colorlinks=false to have any effect) pdfborderstyle: keys for the pdf borderstyle dictionary.  I don't know what keys and values exist for this dictionary, but I do know that pdfborderstyle={/S/U} or pdfborderstyle={/S/U/W 1} can change the link border from a box to an underline.   But it seems impossible with this key structure to have colored links (requiring colorlinks=true and colored borders (requiring colorlinks=false.)  Here is a minimal (non)-working example ():  \documentclass{article} \usepackage{xcolor} \usepackage{hyperref}  \hypersetup{colorlinks=false,linkbordercolor=red,linkcolor=green,pdfborderstyle={/S/U/W 1}}  \begin{document} \section{To See}\label{tosee} \vskip2cm \hyperref[tosee]{just to see} \end{document}   With colorlinks=false (the default), the text is black and the border is red.  With colorlinks=true the text is green and there is no border. What is the number of triangles with integer sides, given the length of the longest side? Suppose $a,b,c \in\mathbb N$, and the value of $c$ is known and fixed, while $a$ and $b$ are unknown and are both smaller than $c$. What is the total number of unique triangles possible with $a, b$ and $c$ as its sides? Wrapped hexagon topology When a square is wrapped at the edges, obtains a torus. Is it possible to do the same for a hexagon?  What is the shape/topology of wrapping a hexagon?     Note: I was just reading this  and came up with this question. I'm a physicist. On this link (Sentinel1  for a SLC product), the resolution is written as a range from the highest corresponding to low incidence angle, to the lowest resolution corresponding to high incidence angle.  My question is how is the resolution related in general to the incidence angle? And if they are really related, why is the resolution affected by the change in the incidence angle? How to create id with AUTO_INCREMENT on Oracle?