I want to convert a mathematics document to pdf, but I am getting missing $ errors.  Here is my code:   \documentclass{article} \begin{document} 1. All prime numbers are odd  Universal Statement: For all x \in \mathbb{N} such that for any a,b \in \mathbb{N} x = ab where a or b must be equal to 1 and for any k \in \mathbb{N}, x = 2k + 1  Counterexample will comprise of: A counterexample will be an x \in \mathbb{N} such that there exists a k \in \mathbb{N} such that x = 2k  Counterexample: 2   6. For all real numbers x, we have x^2-2x+2 &gt; 1  Universal Statement: For all x \in \mathbb{R}, we have x^2-2x+2 &gt; 1  Counterexample will comprise of: A counterexample will be an x such that x^2-2x+2 &lt; 1  Counterexample: 1   14. For all functions f : \mathbb{R} \rightarrow \mathbb{R}, if f is not increasing, then it must be decreasing.  Universal Statement: For all functions f : \mathbb{R} \rightarrow \mathbb{R} for all x_1, x_2 if x_1 &lt; x_2 and f(x_1) \ngeq f(x_2) then f(x_1) \leq f(x_2)  Counterexample will comprise of: A counterexample will be a function f such that for all x_1, x_2 if x_1 &lt; x_2 and f(x_1) \ngeq f(x_2) then f(x_1) \nleq f(x_2)  Counterexample: None, the statement is true  \end{document}
Beginner here with an issue on a simple presentation using beamer  \documentclass{beamer}  \begin{document} \begin{frame}   \tau \epsilon \chi \end{frame} \end{document}   The above fails with the message "! Missing $ inserted." and waits for me to do something when converting to pdf. I have tried adding the instruction \usepackage[utf8]{inputenc} and also \usepackage[greek]{babel}. I have not seen references either to needing to use any other package. What is exactly I am missing?
How to control fan speed? How can I control the computer's fan speed?  On Windows there is a wonderful program called . Undergraduate classical mechanics introduces both Lagrangians and Hamiltonians, while undergrad quantum mechanics seems to only use the Hamiltonian. But particle physics, and more generally quantum field theory seem to only use the Lagrangian, e.g. you hear about the Klein-Gordon Lagrangian, Dirac Lagrangian, Standard Model Lagrangian and so on. Why is there a mismatch here? Why does it seem like only Hamiltonians are used in undergraduate quantum mechanics, but only Lagrangians are used in quantum field theory? Sometimes you spend a day or more solving a technical problem, and when you finally solve it, you may want to post it on your blog (if you have one) to share with the community.  However, most developers don't have a lot of time to update their blogs, and that is why personal blogs are not ranked very highly on Google/Bing.  So even if you describe a brilliant idea, chances are that, except a few of your friends, nobody will ever find it. This is a common reason why some developers start their blogs and soon give up; it is not interesting to write for the community if you have no feedback on your posts.  Unlike personal blogs, Stack Exchange sites are highly ranked in Google (I was amazed when I saw that a question asked on SO just an hour ago appeared 3rd in my Google search!), so if your question and answer are valuable for others, they will be rated highly and will be visible for other developers.  With this in mind, is it good practice to post a question and answer it yourself immediately when you want to share an idea with the community? Clipping raster with mask in QGIS gives AAIGrid error? Change Recycling Bin Location I have a SSD as a primary hard drive, and one HDD for storage. I want the recycling bin to be on the HDD. I want is so that even if I delete files from the SSD the end up on the HDD's recycling bin. What is the proper way of going about this? Inconsistent accessibility error with the following c# code. Why? How to add and sync folders outside SkyDrive folder? I have folders with documents all over my hard drive, some which I would like to include in SkyDrive without moving them into the SkyDrive folder.  E.g. my SkyDrive folder is in C:\Users\Name\SkyDrive, but I have some files in C:\Users\Name\SyncMePlz that I also would like to be synced with SkyDrive so that I can reach them from other devices.  How can this be achieved? Is $7$ the only prime followed by a cube? Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$ How to extract img src, title and alt from html using php? I would like to create a page where all images which reside on my website are listed with title and alternative representation.  I already wrote me a little program to find and load all HTML files, but now I am stuck at how to extract src, title and alt from this HTML:  &lt;img src="/image/fluffybunny.jpg" title="Harvey the bunny" alt="a cute little fluffy bunny" />  I guess this should be done with some regex, but since the order of the tags may vary, and I need all of them, I don't really know how to parse this in an elegant way (I could do it the hard char by char way, but that's painful). In GMAIL you can list all your boss-tell-off and wife-cuss-out emails by clicking Drafts    I'd like to see my started-but-never-finished responses, possibly between x Answers and y Votes in /&lt;&lt;user&gt;&gt;/Stats/? Time dependent Schrödinger equation with time independent potential and separation of variables suppose we have a potential that's independent of time $V(x,t) = V(x)$ so in Schrödinger equation we get: $$i\hbar \frac{\partial \Psi (x,t)}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi (x,t)}{\partial x^2}+V(x)\Psi(x,t)$$ since the LHS involves a variation of $\Psi$ with $x$ and the LHS involves a variation of $\Psi$ with $t$ can we say that a basis for the solutions will be with the form $\Psi(x,t)=\psi(x)T(t)$? Somewhere on Stack Exchange I saw the equation     $$\gcd(2^m-1,2^n-1)=2^{\gcd(m,n)}-1.$$   I had never seen this before, so I started trying to prove it. Without success...  Can anyone explain me (so actually prove) why this equation is true?  And can we say the same when replacing the '$2$' by any integer number '$a$'? A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?  I am really confused by this problem. My first initial thought was to do:  (5 chose 7)(7 chose 0)/ (12 chose 7)  I am not 100% sure about this though. Trigonometry and algebra question Given:   The total length of ad + dc The lengths of each ab, bc and ca That angle adb = angle cdb   How can I work out lengths ad and cd 'Search on Yammer' link in search center refiners I have a heavily branded site I'm working on and can't find where the "Search on Yammer" link is being populated from. It appears within the search refiner/filter web part in the left column but none of the display templates reference this.   I'd like to be able to customize the link, placement on the page, etc. without resorting to jQuery to move elements around the page.     And the markup coming through looks like this. The refiners themselves come through a series of display templates but the Yammer link is nowhere that I can see in any of them.   &lt;div webpartid="f09e98eb-6dc3-4a9b-8dbf-65d0fbc7b7c3" haspers="false" id="WebPartWPQ4" width="100%" class="ms-WPBody " allowdelete="false" style=""&gt;     &lt;div class="ms-ref-ctrl"&gt;         &lt;div class="ms-ref-refiner"&gt;             &lt;div id="Container"&gt;                 &lt;h2 class="ms-displayInline"&gt;                     &lt;a class="ms-ref-name ms-displayInlineBlock ms-srchnav-link-selected ms-link" href="javascript:void(window.open(                     'https://www.yammer.com/search?trk_event=o365_search&amp;amp;search='+                     encodeURIComponent(Srch.ScriptApplicationManager.get_current().queryGroups.                     Default.dataProvider.get_currentQueryState().k),'_blank'));" title="Open a new tab to search for this on Yammer"&gt;Search on Yammer&lt;/a&gt;                 &lt;/h2&gt;             &lt;/div&gt;         &lt;/div&gt;     &lt;/div&gt; &lt;/div&gt; &lt;div componentid="ctl00_SPWebPartManager1_g_f09e98eb_6dc3_4a9b_8dbf_65d0fbc7b7c3_csr" id="ctl00_SPWebPartManager1_g_f09e98eb_6dc3_4a9b_8dbf_65d0fbc7b7c3_csr"&gt;             ... refiners populated through display templates ... &lt;/div&gt; I've had  on the web since 1999, and I'd like to add a page on why complex numbers are (or should be) considered to be numbers.  I'm frequently asked that question.  This is not a question about the existence or usefulness of complex numbers as they do exist as mathematical entities and they are very useful.  It is a question about what makes them numbers.  It could be broadened to ask what constitutes numbers, but I'm specifically interested in complex numbers.  Perhaps it's just historical and sociological, but I'm hoping for an answer that there's something intrinsic about complex numbers that makes them fit into the category of number. How do I unlock privacy in multiplayer modes mission settings? What does this phrase from The adventures of Tom Sawyer sentence mean: "True, the knife would not cut anything, but it was a "sure-enough" Barlow, and there was inconceivable grandeur in that -- though where the Western boys ever got the idea that such a weapon could possibly be counterfeited to its injury is an imposing mystery and will always remain so, perhaps."  Thank you! How to make a surface with a transparent background in pygame