Question is in the title. It appears obvious at first glance, but I've got no idea how to prove it.   Edit: I am referring to the Riemann integral.
Suppose $f:[0,1] \to (0,\infty)$ is a Riemann integrable function. Prove that the integral of the function from $0$ to $1$ is strictly positive.   I have been trying to do this for awhile but I can't seem to get it. Here is my thought process: If the function is Riemann integrable, then its set of discontinuities has measure zero (Lebesgue). I am not sure how to connect this to the integral being positive
Drag and drop not working inside Nautilus on Ubuntu 17.10 Show that if the smallest prime factor $p$ of the positive integer $n$ exceeds $\sqrt[3]{n}$, then $\frac{n}{p}$ must be prime or 1.  I'm stuck trying to prove this. I tried this using contradiction, but I haven't been able to prove it.  My approach:  Let $p$ be the smallest prime factor of the positive integer $n$.  Let $p &gt; \sqrt[3]{n}$  Then we must show that $\frac{n}{p}$ is either a prime number or 1.  We know that $n = pe$ for some $e \in \mathbb{Z}$.  Thus, $\frac{n}{p} = e$  We also know that $p$ > $\sqrt[3]{n}$, so $p^3 &gt; n$, and $p^2 &gt; \frac{n}{p}$  So, assume $\frac{n}{p} = e$ is not prime nor 1, meaning it's a composite number. Let's try to get a contradiction.  If $\frac{n}{p}$ is composite, then $\exists a,b \neq 1: \frac{n}{p} = ab $  Now, here's where I get stuck. What can I do with this info? $\frac{n}{p} = ab $ and $p^2 &gt; \frac{n}{p}$. Ubuntu 14.04 has visual artifacts and freezes I have an equation contained inside \[...\], which automatically makes a \sum with sub- and superscripts turn big--so that the summation sign looks awkward inside parenthesis.  Any idea how to make the parenthesis completely enclose the whole summation?  \documentclass{article} \begin{document} We have: \[ \sum_{i=1}^n i = (\sum_{i=1}^{n-1} i) + n = \frac{(n-1)(n)}{2} + n = \frac{n(n+1)}{2} \] \end{document} Where do I find out how a command/environment is defined? Say I want to redefine the itemize environment, or make a modified version of it. I want to know how it is currently defined. Where do I find this information? If it's some particular package command, I can just look at the .sty file for that package, but if it's something more basic, I don't know where to look...  Is there a reference manual of where all this stuff is explained? Or is there a file in the depths of my texmf tree I should poke around in? Why aren't all the badges shown on the track menu? I like using the 'Track Badges' menu on my profile a lot (I know what you're going to say, I just have a knack for these things), but I keep noticing something a bit unusual.  Many of the Badges featured on the actual list do not get featured on this menu. For example, I've been hoping to be able to track progress for the Pundit badge (ten comments with score of five or more), but it doesn't show up in the menu.  Why not? I am aware that the "Eye of Sauron" in Peter Jackson's movies was not Sauron's actual physical form.  What the answers at '' don't indicate is, despite this, what abilities of vision Sauron may have had.  Did he have the ability to see from afar? If so, what are his limitations or details of this power? Is it some kind of Elvish-sight like Legolas but stronger? Was it a magical power? Or perhaps with the help of the Palantir (I'm not sure of this last one because I dont remember if the Palantir could only see what other Palantíri were seeing or anything he wanted)? Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$, $\forall x\in G$. Prove that $H$ is a normal subgroup of $G$.    I have tried to using the definition but failed. Can someone help me please. Do we need inertial frames in Lagrangian mechanics? I was just looking at the statistics for migrated questions in the  mod tools, and noticed this oddity:    The actual statistics, as visible to any 10k+ SFF user , are: 6 migrated to Worldbuilding, 2 to Literature, 2 to SFF meta, 1 to Movies &amp; TV, 1 to Writers, and 1 to Aviation.  Why is one of the meta migrations showing up with a blank icon rather than with the other?  Both migrated questions were closed as duplicates on meta. Both were migrated by 5 community members without mod involvement. One of the stubs on main has since been deleted, but so have the stubs for some of the other migrated questions. I can't think of anything to explain this discrepancy. Sharepoint 2010 - Deploy webpart as Feature scope = web I want to create and deploy a web part as web-scoped feature.  In Visual Studio 2010, when I make the feature scope=web, I cannot add the webpart to that feature as I am able to do when scope=site. find exclude directory How do you performance test JavaScript code? Nested Virtualization What I do: I want to write a kernel module that does stuff to the KVM data structures. But I don't want to run it on the real machine, so I run one guest, inside it I run another two guests, and want to test my module.  The problem: VirtualBox (which now runs the outer guest), doesn't support nested virtualization, and when I cat /proc/cpuinfo | grep vmx I get no output.  What can I use that has nested virtualization?  You may look at my  to get an idea of what I want to do. Is there any way to specify a suggested filename when using data: URI? If for example you follow the link:  data:application/octet-stream;base64,SGVsbG8=  The browser will prompt you to download a file consisting of the data held as base64 in the hyperlink itself.  Is there any way of suggesting a default name in the markup?  If not, is there a JavaScript solution? Disable chat migration notification if one of the users has insufficient rep? Simple request, really.  Can we add a detection for the     Please avoid extended discussions in   comments. Would you like to   automatically move this discussion to   chat?   prompt, so that if one of the users in the "extended discussion" has under 20 rep it doesn't appear?  I think a lot of the users this apply to will have low rep and it may take some back and forth to get good info out of them.  New suggestion: how about if a sufficiently high-rep user is clicking on the link, the low-rep user gets a field promotion sufficient to chat? Low-rep users are particularly prone to post questions to lead in this direction of needing to move to chat. When a lattice is a lattice of open sets of some topological space? When a lattice $(L,\leqslant)$ is a lattice of open (or closed) sets of some topological space $(X,\tau)$? Which conditions have to be satisfied? We may assume that $X$ is $T_1$. Is a 2-hour transit time enough to catch a connecting flight in Muscat airport? Both flights are with Oman Air I am flying from Dubai to India with Oman Air with a layover of 2 hours at Muscat airport. Is 2 hours enough for me to catch my connecting flight from Muscat to New Delhi? My flight from Dubai to Muscat as well as the connecting flight from Muscat to New Delhi are with Oman Air. Do I need to re-check in my luggage? Am I taking a risk or should I take an earlier flight from Dubai to get more layover time to be on the safer side? When a function has a specific-size array parameter, why is it replaced with a pointer? Why are lamps and mesh lights not illuminating anything?