Use of comma with "of course"
Need a comma before an adverb as last word in sentence?
I'm new here. Can anyone give me a hint in this problem? Please.  Let $X$ be a topological space. If $f,g$ are continuous function of $f,g\colon X\to S^n$  which $f(x)\neq -g(x)$ for all $x$ in $X$, show $f$ and $g$ are homotopics. I try to show a homotopy using $$q(x) = \frac{f(x)+g(x)}{\|f(x)+g(x)\|}$$ it's well defined, but i'm stuck. Cross-site AJAX requests I need to make an AJAX request from a website to a REST web service hosted in another domain.  Although this is works just fine in Internet Explorer, other browsers such as Mozilla and Google Chrome impose far stricter security restrictions, which prohibit cross-site AJAX requests.  The problem is that I have no control over the domain nor the web server where the site is hosted. This means that my REST web service must run somewhere else, and I can't put in place any redirection mechanism.  Here is the JavaScript code that makes the asynchronous call:  var serviceUrl = "http://myservicedomain"; var payload = "&lt;myRequest&gt;&lt;content&gt;Some content&lt;/content&gt;&lt;/myRequest&gt;"; var request = new XMLHttpRequest(); request.open("POST", serviceUrl, true); // &lt;-- This fails in Mozilla Firefox amongst other browsers request.setRequestHeader("Content-type", "text/xml"); request.send(payload);   How can I have this work in other browsers beside Internet Explorer? Why is the notation $\frac{\partial f}{\partial x}$ used? Can I prevent enumeration of usernames on my wordpress site? I can see users at the moment using the WPScan tool. What amp rating of 24vac transformer for LM317T? I want to know what size transformer for LM317 at full 30 VDC. I know its a 24 VAC center tapped transformer but is 1 A or 5 A transformer best suited for a linear power supply of 1.5-30 VDC?  I will be using a standard LM317 variable power supply circuit with the 2200 uF 50 V smoothing and the 240 ohm drain resistor and potentiometer. I have a homemade oversized aluminum heat-sink that is quite large. Why does logging in to Stack Overflow keep me signed in to my Gmail email after logging out and regardless of the Stay signed in checkbox?  Steps to reproduce:   Browse to  and confirm you are logged out Browse to  and confirm you are logged out Click login Click Google Enter Email/Password and confirm Stay signed in is unchecked Click Sign in Click logout (up top) Click Logout (down below) Browse to  and confirm you are still logged in Click Sign out &lt;- Shouldn't clicking Logout on Stack Overflow be doing the same thing as this? Browse to  and confirm you are logged out     Answers are making sense but my frustration is that clicking Logout (twice) on StackOverflow essentially does nothing. If I proceed to click login and Gmail I am immediately authenticated because I still have an active Gmail cookie. In order to effectively logout I need to click Logout twice on Stack Overflow and then manually browse to  and Sign out. Is it possible for an American to get a Chinese visa in Hong Kong? Mapping Russia - Int'l dateline splitting polygon In Windows there’re perhaps only a couple of important folders (by important I mean important in my logical picture of the Windows file system) in the installation drive (in my case C:\). Namely Program Files and Windows. I simply stay away from Windows folder and the “add remove program files” is good enough to handle the program files folder of Windows. Of course there’s a folder named Users where the users (who are not admins) can access only their folders.  Thus there’s a clear picture at some level in my mind of the Windows file system. In Ubuntu, when I reach the location /, there’s a huge list of folders, most of which I have no clue as to what they contain. The /bin folder seems to be the equivalent of the Windows folder in windows. The /usr folder seems like it’s the equivalent of the Users folder in Windows. But even the /home folder looks like it can fit the bill.  Please understand that I do understand, that Ubuntu (Linux) has a different character than that of Windows, i.e., there need not be exact equivalent of Windows functions, in Ubuntu. All I am looking for is a bit more clearer picture of the Ubuntu file system.   This question is a part of a bigger question which I am splitting up to make it more answerable. The original question can be found here: I am currently using 19.04 and I got "No new release found for 19.10" I tried logging in with a Google account, but I got the following error: Automating the scanning of graphics files for corruption Does anyone know of a way to check graphics files (particularly JPEG, GIF, and PNG) for corruption (preferably in an automated way)?    Explanation:  A few days ago, a command worked incorrectly and ended up deleting thousands of graphics files from a FAT32 volume that was practically out of space. I’ve used several different file/photo-recovery programs, but naturally, they are limited in how much they can recover (though fortunately the volume has 8KB clusters, which helps somewhat).  Anyway, some of the larger files, that were fragmented, are now corrupt. Some of them are not even real files at all (the recovery software merely dumped the clusters that were pointed to by now-overwritten directory entries), while others are broken because of fragmentation.  Moreover, because some picture formats embed a smaller version of the picture as a thumbnail, scanning the thumbnails for corruption is not reliable because it may be intact while the actual file (i.e., the picture when viewed full-size), could be corrupt.    Here are a couple of examples:      Here’s the second one. It’s so damaged that it doesn’t display anything.    (A third one wouldn’t even upload because it doesn’t even have the correct header!) Check if user is using IE Moving all files to a new computer, my concern is links I have a UK Refugee passport. Do I need a visa to go to France?   I want to go for two days with my husband, but I'm not quite sure if I can go without a visa. Creating a large amount of convex polygons using existing coordinates Conjugating verbs for nouns referring to groups of people Possible Duplicate:          Frequently when reading tech articles, I see sentences like "Microsoft have released ..." or "Apple have announced ...". This seems wrong to me because the nouns are singular; Microsoft and Apple are individual companies, even though they refer to groups of people. I have not seen this usage outside of tech journalism, but it's pervasive enough that it makes me wonder: is this actually the correct usage?  As a follow-up question, is it correct to use a plural pronoun for a singular antecedent like this? For example, "Apple has announced they are changing their name to Orange" or "Apple has announced it is changing its name to Orange". The second form seems technically correct but sounds awkward. Exact relationship between electric field and intensity I often see $I(t)\propto |E(t)|^2$. What is the exact form ? Which constants are missing to make this an equality and why are they so often omitted ? What are valid values for the id attribute in HTML? Living forever in D&D (via spells)? I was thinking of a way for a humanoid (PC or NPC) to live forever in a D&amp;D setting, but through rather "common" and reproducible means, such that they will be available to many. By this logic I exclude cases such as a god giving immortality (or some other intervention) or a unique item granting an endless lifespan etc.  To cover all bases I will note that miracle and wish cannot do this directly, nor can true resurrection (and its lesser brethren) "restore to life a creature who has died of old age".  I had came up with the following ruse:   Reach your deathbed with at least 2 HD (or levels). Have someone kill you so that the cause of death will not be "old age". Have a druid cast reincarnate on you into a young body. You "recall the majority of your former life". I assume your memories, personality/identity and experiences are preserved.   Rinse and repeat. It's not that difficult to recover the 1 HD lost through the course of almost a lifetime. The material components are worth 1,000 gp - might not be easy to get, but surely possible.  Furthermore, it is stated that "A wish or a miracle spell can restore a reincarnated character to his or her original form.". I assume the "original form" is the aged humanoid at his or her deathbed - not the direction we are looking for, unless it means that the humanoid restores his race only.  Is there a flaw in this plan? Is there another way of doing it?