What does this ".=" mean in perl
What does dot-equals mean in Perl?
Append to the end of a file in C I recall from complex analysis a while ago that the series $$\sum_{n=1}^\infty \frac{z^{n!}}{n}$$ has radius of convergence 1, diverges on roots of unity, and converges elsewhere on the circle. It's simple enough to see that it has to diverge on roots of unity: consider $z$ such that $z^k = 1$ for some $k \in \mathbb{N}.$ Plug this into the series and you see that past the $k$'th term, $z^{n!} = (z^k)^m = 1$ for some $m \in \mathbb{N}$; hence, the series becomes harmonic and must diverge.  But I don't recall how to show that the series converges for other values on the circle. If this is simple I'd like just a hint, if it is involved I would prefer a sparse outline of the proof. Thank you! Does Moore's law apply to quantum computing? Plain and simple. Does  apply to quantum computing, or is it similar but with the numbers adjusted (ex. triples every 2 years). Also, if Moore's law doesn't apply, why do qubits change it? "Where" in careers' search seems to be broken Let's say I want to find a company in Ontario, Canada. Ok, I navigate to company pages and type ON, Canada to Where in search:        but there are no companies in there. So why if I type just Canada it finds companies in ontario; and if I type specific area (ON, CA)  it doesn't find anything ? How do I learn where the source file for a given Python module is installed? Is the method different on Windows than on Linux?  I'm trying to look for the source of the datetime module in particular, but I'm interested in a more general answer as well. How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. Reference to a figure uses the section's number Ubuntu 18.04 opening system settings logs me out Why time is considered a dimension? Getting opencv error in c++ Subject/Complement Agreement. How to describe problem with "The thing is the objects." In my , I provided the following, problematic,  wording (especially bold italic), and I need help to better understand this issue so I can fix my answer:1          The thing is the books. (Reduced form of Sentence 2.a)         Fundamentally, Sentence 2.a (the so-called "correct" answer), is grammatically defective. Recall there is another grammatical rule: the subject and subject's complement should match in number.    A clarification is needed here. I am not suggesting here, in this EL&amp;U question, that there is any such singular grammatical rule as indicated in the quote above.  The quote continues as follows:     The reduced sentence makes the disagreement between the subject's and complement's plurality obvious. What is one to do? Language is linear and we know "The thing is X" is better than "The thing are X", so we go with the former, which is the subject-verb agreement rule. But what is "the books" then? It must be thought of as a collective noun, even if it doesn't look or feel like one. Forcing something to be a collective noun is related to the idea of notional agreement.   Others noted that grammatically defective is too strongly worded.  There is no such "grammatical rule" for subject/complement agreement.  Please help me understand/improve upon my line of thought here.  I'm stating that Sentence 2.1 presents a fundamental "conflict" or "error" (however one might define error) at some level (morphological, syntax, grammatical, semantic):     The thing is the books.  (Or, "The thing is the objects.")   Based on the "obvious" morphosyntactic plurality conflict, the above sentence feels so wrong that I think many native speakers would think it "simply" grammatically incorrect. However, @F.E. gives counter examples:     And here are some more grammatical examples, where the number of subject and predicative complement don't agree: "They were a problem to us all", "That so-called work of art is simply four pieces of driftwood glued together" (CGEL, page 254-5). As CGEL says: "What is required is semantic compatibility, not syntactic agreement . . .". There are more examples on page 512: "The only thing we need now is some new curtains", "The major asset of the team is its world-class opening bowlers", "Our neighbors are a nuisance", "This gadget is five different tools in one".   I think all the examples given above can be explained as notional agreement.    Question 1: If we explain this phenomena in terms of notional vs syntactic agreement, where does "grammatically correct/incorrect" fit in?  Question 2: Can a simple sentence such as "The thing is the objects." be grammatically incorrect while more complex sentences such as "The thing is four pieces of driftwood glued together." be grammatically correct?  (The answer, in my mind, must be no; this is my conundrum.)  Question 3: Would it be better to say that Sentence 2.a has a low level of (linguistic) ?   Question 4: How about a low level of  and that it's semantically difficult to be (linguistically) ?    Question 5: Do we simply draw a hard line and say "The thing is the objects." is 100% grammatically correct?  I didn't particularly like this option based on intuitive notions of "grammatically correct".    1. Please help me and be kind; I'm trying to improve my understanding. I'm looking for cool, objective advice on how to look at this.  I numbered my questions so they can be easily referenced, if desired.  My preference is the final answer would sufficiently answer all the questions, but of course that can be done explicitly or implicitly. 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. How much of 32-bit support is dropped in macOS Catalina? macOS Catalina is said to have dropped support for 32-bit apps. It’s not clear how much support is dropped.   Is there any supported way for a 64-bit app to request the kernel to create a 32-bit code segment? 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());     } } l, ls & la -- what are the differences, and are there more of these commands? You can't see the question owner's special color When the owner of a question comments on their question or an answer to their question or self-answers their question, they get a special color for the box around their username.  The problem is, you can't see the box:        Can you please make this not white on white? Resizing an Image without losing any quality Reference book on measure theory I post this question with some personal specifications. I hope it does not overlap with old posted questions.  Recently I strongly feel that I have to review the knowledge of measure theory for the sake of starting my thesis.  I am not totally new with measure theory, since I have taken and past one course at the graduate level. Unfortunately, because the lecturer was not so good at teaching, I followed the course by self-study. Now I feel that all the knowledge has gone after the exam and still don’t have a clear overview on the structure of measure theory. And here come my specified requirements for a reference book.   I wish the book elaborates the proofs, since I will read it on my own again, sadly. And this is the most important criterion for the book. I wish the book covers most of the topics in measure theory. Although the topic of my thesis is on stochastic integration, I do want to review measure theory at a more general level, which means it could emphasize on both aspects of analysis and probability. If such a condition cannot be achieved, I'd like to more focus on probability. I wish the book could deal with convergences and uniform integrability carefully, as Chung’s probability book.    My expectation is after thorough reading, I could have strong background to start a thesis on stochastic integration at an analytic level.  Sorry for such a tedious question.  P.S: the textbook I used is Schilling’s book: measures, integrals and martingales. It is a pretty good textbook, but misprints really ruin the fun of reading. I'm building an application where I should capture several values and build a text with them: Name, Age, etc.   The output will be a plain text into a TextBox.  I am trying to make those information appear in kind of columns, therefore I am trying to separate them with tab to make it clearer.  For example, instead of having:  Ann 26 Sarah 29 Paul 45   I would like it to show as:  Ann tab 26 Sarah tab 29 Paul tab 45  Any tip on how to insert the tabs into my text? Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$