Is there a way to write a blackboard version of the Greek capital letter Omega in LaTeX?
The blackboard bold font in the AMSFonts package only has capital letters.  I sometimes wish to use a blackboard bold "1", for which I can use \usepackage{bbold}. But this changes the entire blackboard bold font, and I like the original AMSFonts versions of the capital letters better.  Is there a simple way for me to get \mathbb{1} from one package and the blackboard bold capitals from another?
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit Basic photo editing on OS X All of a sudden, without any change in the index.html, our site is showing up in Google search results (on multiple browsers and devices) with Google Preview text that, instead of giving a summary of our site, now says:     Your browser does not currently recognize any of the video formats available. Click here to visit our frequently asked questions about HTML5 video.     We have a YouTube embed on our homepage that does include an html5 parameter in the media URL link in the embed, but there are no issues playing the video with any browser and device we can find.  What would suddenly cause this text to appear in Google search results?   We are using the  tags as the metatags in the &lt;head&gt; of our webpage and do indeed have title and description tags.    To mimic the behavior of Googlebot, I installed Windows on a VM and got Chromium 41 running. I get the same Google Preview text with the html5 video message when the site comes up in Google search results using this browser.    When I view the site in Chromium 41, I see the YouTube embed and it renders on the page and plays with no issue, just as with all other browser and devices we've tested on. The only time we see this message is in the Google search results, not on our actual site. How do I install the Firefox Developer Edition? What is the dot product and why do we need it? I understand how to calculate the dot product of the vectors. But I don't actually understand what a dot product is, and why it's needed.  Could you answer these questions? We know that $221 = 17*13$. So we can check if the system has roots to both of those equations separately, which it does:  $x^{5} \equiv 2$ mod $13$ has the solution $6 + 13n$ and $x^{5} \equiv 2$ mod $17$ has the solution $15 + 17n$.   I got these numbers from wolfram, I have no idea how to solve this problem WITHOUT a calculator. And even after finding these numbers. How would one obtain a solution modulo $221$? I was thinking the Chinese Remainder Theorem but I am under the assumption that CRT only applies to problems with powers of $x$ which are $1$.  Thanks. How to set render engine in blender? Persistent live drive with a partition for persistence There are some web sites describing  new tools new features in [new versions of] old tools  that can create a persistent live drive from an iso file with Ubuntu 19.10 and the corresponding Ubuntu family flavours.  Why and how does it work? How is it different from earlier methods for persistent live drives? Isn't live the default for a cloned drive? Why cannot a set be its own element? Under what conditions will healers switch targets? I've been using healers lately, which I haven't really utilized much before. I've noticed that they will sometimes switch targets, even when their original target still lives.   What conditions are needed for healers to switch targets? Use of “f ” instead of “s” in historic, printed English documents I was at a museum in London yesterday, and one of the items on exhibit is a document from the eighteenth century. It uses the letter f a lot where s should be used—for example, in Majefty.     Did the letter f once have the same sound as s today, or were some of those words actually spoken with an f ? Can someone remind me of the name of the author, the name of the hero and the name of the series if any? Adventure Sci-Fi books, short by today's epic standards ( = about same length as Heinlein's shorter youth books), probably published late 50s?, early 60s? by Bantam? or Del Rey? I think at least 30, possibly more than 40 books in the series. Not comic books. The author is not a well-known writer. At least, I don't remember seeing the name on any other books, ever.   Subject: a man who can move and respond to threats extremely fast learns about a secret potion that allows a person to change bodies with someone else and thus control them. A powerful organization does not want the secret to be known, because they use the potion to control politicians on many planets. The organization's goons are people who had surgeries to remove their emotions, and function like organic computers. They can communicate over interstellar distances and follow and murder anyone who learns the secret. I remember the following detail about the potion: there are two nearly identical molecules that have to be assembled in a certain sequence. Two of the components had to be switched around and that determined who would be dominant and who would be controlled during the mind switch / body swap.   Every book finds the hero on another planet with new adventures, and usually taking another deep-sleep-passage to another world, fleeing his pursuers. The background story about the secret potion is dished out little by little in each book.  One book in the series starts like this: hero is on very hot planet, diving for valuable marine life, catches a deadly fungus disease and is rescued last moment in exchange for his catch...  One of the themes that returns often is that the hero is an excellent knife fighter.  Of course he's a womanizer. In the second (or close to 2nd) book in the series, he's involved with a woman who rules a planet.  To travel to another world, he usually takes the cheapest dead-sleep passage, and there's always a 10-25% risk you won't wake up from that. Can you make an opportunity attack against a moving object? Unexpected gaps in IDENTITY column Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$ The cardinality of the set of all finite subsets of an infinite set How to have full bleed between two facing pages Indesign Often in fantasies involving magic casting spells requires a certain physical or mental toll on the caster. I don't recall any mention of spells being physically or mentally taxing in the Harry Potter universe.  Does this mean they can cast an unlimited number of spells in a given day without any negative effect to themselves? How do I deal with a bored or distracted player bringing down the group? My group have been playing various D&amp;D style games for a few years,  I have one player however that often will drift off and start playing on his phone  and several times has actually fallen asleep (with his character having to be "nudged" along by his fellow players).  He insists he's "just tired" and "isn't bored" — and besides, he keeps insisting we all get together for D&amp;D and wants to play.  Unfortunately we're all pretty busy, so if I'm to get the group together at all it's usually late on a Sunday. After talking to the player he insists it's not the game, or the story, he just happens to be tired. But, it's the same excuse every week, and the odd times we've played at different times or situations, the falling asleep has happened.  How do I cope with:   The morale destroying (for me) idea of your players falling asleep through a campaign and story you've put lots of work into. The general tone of the room when this player loses interest. (Occasionally a couple of others zone out into Facebook when they're not "active" because the players have split up / gone unconscious).   Given that it's an "all or nothing" situation with the group (there are only 3 players and they won't play unless all 3 are around), how do I best deal with it? Evaluation of $\lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}n^n}$ without stirling approximation Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}\cdot n^n}$   $\bf{My\; Try::}$we can write it as $$l=\lim_{n\rightarrow \infty}\frac{e^n}{\sqrt{n}}\cdot \left(\frac{1}{n}\cdot \frac{2}{n}\cdot \frac{3}{n}\cdots \cdots \frac{n}{n}\right)$$  $$\ln (l) = \lim_{n\rightarrow \infty}\bigg[n-\frac{1}{2}n+\sum^{n}_{r=1}\ln\left(\frac{r}{n}\right)\bigg]$$  Now how can i solve it, Help required, Thanks