There exists a sequence of Riemann integrable functions on [0, 1] whose pointwise limit is not Riemann integrable
An example of a sequence of Riemann integrable functions $(f_n)$ that converges pointwise to a function $f$ that is not Riemann integrable.
Intellisense in IntelliJ no longer working Can we use media9 to show a video on a PDF but the video is not embedded to the PDF? I have video tutorials that I want to show in my presentation with beamer class. I don't want the video files get embedded to the PDF because they will make the PDF size very very huge.  If you know how the videos can be played on the HTML with a reference rather than embedding the video file to the HTML file, I want something like this to be applied to my PDF presentation. I just want to reference the video URL from my PDF presentation.   Shortly speaking, can we use media9 to show a video on a PDF but the video is not embedded to the PDF?  Uploading those videos to a web server might be difficult for me because internet connection is very slow and sometimes not available in the presentation room. :-) "Less" vs. "fewer" I've just received a memo which says (effectively)      As more people leave, there will be less people available.   I want that word to be fewer. Are there guidelines for which word ought to be used when? 70s or 80s Book. Post Catastrophe, Sheriff tries to hold town together, and keep his schizo wife from killing him Breaking of diffeomorphism invariance after fixing a background metric How do I uninstall Windows 8 and install Windows 7? I have a friend, who just got a new Toshiba Satellite C series with Windows 8. I tried to uninstall Windows 8 and install Windows 7 but was unable to do so.  I did everything I could:   Boot disk - would not load (error message Media -- Fail) Boot USB - would not load (error message Media -- Fail) Loading Windows 7 disk from system, fails with different errors   Does anybody know what I can do in order to install Windows 7? Show Kripke's model proving that the following formula isn't tautology in intuitionistic logic. $ \neg ( p \wedge q ) \implies (\neg p \vee \neg q) $  Please help/hint me ;) When we want to open an application or file from the terminal, we type, say,  okular file.dvi   This opens the application, but also shows the status of the application. We cannot close the terminal, because it kills the process. Unfortunately, if you're trying to, for example, create a LaTeX file, you will need one tab for the text editor, one for the dvi file, and so on. And if you're trying to open all windows from the terminal, you can forget it. I'm trying use the terminal as much as possible, and while I have Yakuake, it is still a bother having so many tabs and seeing which of those have an application I've killed and so on.  So, is there a way to open an application/file from the terminal so that the status doesn't show and immediately gives the prompt so that we can use it to open more applications? lualatex MWE not working I was watching , and it got me thinking about when optional parameters are available in C# what is going to be the recommended way to declare methods that do not need all parameters specified?  For example something like the FileStream class has about fifteen different constructors which can be divided into logical 'families' e.g. the ones below from a string, the ones from an IntPtr and the ones from a SafeFileHandle.  FileStream(string,FileMode); FileStream(string,FileMode,FileAccess); FileStream(string,FileMode,FileAccess,FileShare); FileStream(string,FileMode,FileAccess,FileShare,int); FileStream(string,FileMode,FileAccess,FileShare,int,bool);   It seems to me that this type of pattern could be simplified by having three constructors instead, and using optional parameters for the ones that can be defaulted, which would make the different families of constructors more distinct [note: I know this change will not be made in the BCL, I'm talking hypothetically for this type of situation].  What do you think? From C# 4.0 will it make more sense to make closely related groups of constructors and methods a single method with optional parameters, or is there a good reason to stick with the traditional many-overload mechanism? Let $b_n$ be a sequence which decreases monotonically to zero, prove $\sum b_nz^n$ converges for $|z|\leq 1$ and $z\neq 1$.  So I was able to prove it converges on the open unit disk in the complex plane, but except for a few special points on the boundary, such as $-1$ and $i$, where I was able to use the alternating series test, I can't seem to prove it converges in general on the boundary minus $z=1$.  I feel I have to somehow use the fact that all the numbers on the unit circle except $z=1$ rotate around and around as you raise them to higher and higher powers, thus you get the real and imaginary parts of your series to alternate between sets of positive and negative terms, but in a very irregular way for most initial angles.  I tried to simplify the problem by breaking the series into its real and imaginary parts, and then trying to prove they each converge separately, but I still can't prove either converges:  $$\sum_{n=0}^{\infty}b_ne^{n\theta i} = \sum_{n=0}^{\infty}b_n\cos(n\theta) +i\sum_{n=0}^{\infty}b_n\sin(n\theta).$$ I'm using post thumbnails to link to a page.  Is it possible to add a class name to the post thumbnail image.  &lt;li&gt;&lt;a href="&lt;?php the_permalink(); ?&gt;" &gt;&lt;?php the_post_thumbnail(); ?&gt;&lt;/a&gt;&lt;/li&gt; What does the size of the standard deviation mean? According to  (my emphasis),     In statistics, the standard deviation ... is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to 0 indicates that the data points tend to be very close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.   The purpose of the standard deviation (SD), then, is to tell us how varied or uniform (SD → 0) the data is.  So, given a certain SD, how varied is the data? What does the size of the standard deviation mean?  Please explain the meaning of the SD by interpreting an SD = 1 (M = 0).  If you cannot interpret the size (quantity) of this SD, what other information would you need to be able to interpret it, and how would you interpret it, given that information? Please provide an example.  If, on the other hand, the quantity of the SD cannot be qualified in this manner, my argument is that it is essentially meaningless. If you disagree, please explain the meaning of the SD.  &nbsp;    The following are earlier versions to give context to the answers. Unfortunately these didn't really convey what I wanted, and my attempt to ask it elsewhere was closed. (I don't need these versions answered now):  First revision:  What does the size of the standard deviation mean?  For example, if I want to study human body size and I find that adult human body size has a standard deviation of 2 cm, I would probably infer that adult human body size is very uniform, while a 2 cm standard deviation in the size of mice would mean that mice differ surprisingly much in body size.  Obviously the meaning of the standard deviation is its relation to the mean, and a standard deviation around a tenth of the mean is unremarkable (e.g. for IQ: SD = 0.15 * M).  But what is considered "small" and what is "large", when it comes to the relation between standard deviation and mean? Are there guidelines similar to the ones that Cohen gives for correlations (a correlation of 0.5 is large, 0.3 is moderate, and 0.1 is small)?    Original question:  We always calculate and report means and standard deviations. But what does the size of the variance actually mean?  For example, assume we are observing which seat people take in an empty room. If we observe that the majority of people sit close to the window with little variance, we can assume this to mean that people generally prefer siting near the window and getting a view or enough light is the main motivating factor in choosing a seat. If on the other hand we observe that while the largest proportion sit close to the window there is a large variance with other seats taken often also (e.g. many sit close to the door, others sit close to the water dispenser or the newspapers), we might assume that while many people prefer to sit close to the window, there seem to be more factors than light or view that influence choice of seating and differing preferences in different people.  At what values can we say that the behavior we have observed is very varied (different people like to sit in different places)? And when can we infer that behavior is mostly uniform (everyone likes to sit at the window) and the little variation our data shows is mostly a result of random effects or confounding variables (dirt on one chair, the sun having moved and more shade in the back, etc.)?  Are there guidelines for assessing the magnitude of variance in data, similar to Cohen's guidelines for interpreting effect size (a correlation of 0.5 is large, 0.3 is moderate, and 0.1 is small)?  For example, if 90% (or only 30%) of observations fall within one standard deviation from the mean, is that uncommon or completely unremarkable? A high-reputation, highly-active user has already been dinged once for a sockpuppet, and I just dinged him again. He probably has another sockpuppet as well.   What are the guidelines for handling users who game the system in this fashion? Specifically,   How can I be sure I'm looking at a sockpuppet? When should sockpuppets be considered a problem? How should moderators handle problematic sockpuppets once they've been identified? I was suspended for sockpuppetting and feel this is unfair Reason for the current trend to use «she» as the gender-neutral pronoun? There are some questions on gender-neutral pronouns both  and on .  User Christine Letts :     In academia, there is currently a   movement toward using the feminine   pronoun at all times.   I wonder why that is. I came across several examples on papers I read, but the only one I can remember at the moment is a book: Seth Godin's . While some might not be comfortable labeling it as part of academia, it suits my point perfectly. Every time he refers to a person, he uses the feminine pronoun.  User Senseful  the following, potentially identifying affirmative action as the precursor for this trend.     I remember reading somewhere that it   was recommended to use the opposite of   what most people stereotype the   profession as. So, for example, when   talking about a chiropractor, you   would use "her", and when talking   about a secretary, you would use   "his".   So, where do you think this trend comes from? Maximum and Minimum values for ints I took a look at  but my question is not the same.  I have unique keys encrypting each plaintext (in CBC mode, AES-256) and I do not use a key to encrypt more than one plaintext. Is it insecure to use null IVs in this case? If it is insecure, why? I want to show that for each $n \in \mathbb N$ it holds that $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = 2n \frac{n^n}{n!}.$$ But I have absolutely no idea how to do that. I tried to split the series like this:  $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = \sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) + \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n)$$ Now I want to show that $\sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) = \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n) = n \frac{n^n}{n!}$ holds. But I got no idea how to achieve that. I tried to use induction but things became pretty messy and I don't think it will work like that. On the other hand I got the idea that it might have to do with $\exp$ or binomial coefficients but I don't see where I can facilitate that. I would appreciate some hints :) What are the complexity guarantees of the standard containers? Notify instantly when a currently viewed post is deleted At the moment SE shows us current voting results, a notification for new answers and comments, etc., instantly. However, it doesn't show us when a post is deleted.  Please notify us also when a post is deleted. Then I don't have to type a (long) comment, only to notice the post got deleted in the meantime.