Key input lag when typing
Why there is a delay between when a key is pressed and when it is accepted?
Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|<|\mathbb{R}|$, is it true that $X$ is null? Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|&lt;2^{\aleph_0}$, is it true that $X$ is null?  Of course I am not assuming the Continuum Hypothesis.   EDIT: It might be helpful to know that all Borel measurable sets have cardinality either $\aleph_0$ or $2^{\aleph_0}$. Then a measurable set of cardinality strictly between those two must be Lebesgue but not Borel measurable. Why do we need Diffie Hellman? Diffie–Hellman offers secure key exchange only if sides are authenticated. For authentication, sides are using public/private key. So if side A knows the public key of the side B, then A can simply use that key to encrypt the message (or the new session key).  Why bother to use separate key exchange algorithm? Read-only file system I want to derive a closed formula for the integral $$I_n= \int \frac {dx}{\prod_{r=0}^n (x+r)}$$  On writing out first few terms we get   For $n=0$, $$I_0=\ln \vert x\vert+C$$ For $n=1$, $$I_1=\ln \vert x\vert-\ln \vert x+1\vert+C$$ For $n=2$ $$I_2=\frac {1}{2!}\left(\sum_{r=0}^2 (-1)^r\binom {2}{r} \ln \vert x+r\vert\right)+C$$ For $n=3$ $$I_3=\frac {1}{3!}\left(\sum_{r=0}^3 (-1)^r\binom {3}{r} \ln \vert x+r\vert\right)+C$$  Hence for generalized $n$ we have $$I_n=\frac {1}{n!}\left(\sum_{r=0}^n (-1)^r\binom {n}{r} (\ln \vert x+r\vert)\right)+C$$  Now this is just an observation but I want to prove that it is correct. I have tried lot of methods but not useful. Partial fractions would have been most useful but would go out on tedious task which is nearly impossible.  Also integration by parts won't help nor any trig substitution. So any ideas are welcome.  And ya,  this is not a homework question,  it's a question which I just saw in a integral challenge paper. Saving project with data source path as relative in QGIS? Is there an option in QGIS to save the project with the data source being a relative path?  I don't see the option here. QGIS Wroclaw1.7.3 If $x_1,...,x_n$ are positive real numbers and if $y_k=1/x_k$, prove that $$\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2.$$   I've been learning induction, and I've come across this problem that I really can't even break down and begin to think about. I've been told it has something to do with Cauchy-Schwarz, but I cannot figure out how to apply it. I would appreciate help figuring out how to go about and formulate this proof. Thanks! What causes the portraits of Wizards to behave interactively? I found an asnwered question concerning this topic already here:  Copying \captionsetup[subfigure]{justification=centering} doesn't help me thought for I am using different packages.  I would like my Captions and Subcaptions to be justified as the text below. Just under my pictures. Any suggestions?  Thanks a lot  \documentclass{article} \usepackage{subfig} \usepackage[labelfont=bf, justification=justified]{caption} \usepackage[demo]{graphicx}% Remove demo option in real document  \begin{document}     \begin{figure} %   \captionsetup[subfigure]{justification=centering}     \centering       \subfloat[Subcaption one \newline including a linebreak ]   {     \includegraphics[width=0.2\textwidth]{image1}     }     \hspace{1cm}     \subfloat[Subcaption two \newline including a linebreak]     {     \includegraphics[width=0.2\textwidth]{image2}     }        \caption{Figure caption \newline with additional text right here} \end{figure}  \begin{center} This is correctly justified Text \\ including a longer linebreak than blabla. \end{center} \end{document} Will Windows 10's reset delete my Linux partitions? Is there any canon evidence that FN-2187 actually worked in sanitation? Finn tells Han that he worked in "Sanitation" on Starkiller.  FINN The flooding tunnels are over that ridge. We'll get in that way. HAN What was your job when you were based here? FINN Sanitation. HAN Sanitation? Then how do you know how to disable the shields? FINN I don't. I'm just here to get Rey   It just occurs to me - the "I was in sanitation" line given to Han seems to be the only actual canon evidence of "Sanitation" job.   But was it the truth"?!?!  Finn is always trying to create a positive impression of himself with the Resistance, from the get-go:   He tells Poe that he's rescuing him because that's the "Right thing to do" (with Poe quickly seeing through the fib: "You need a pilot!") He tells Rey that he's Resistance (she buys that because she's a romantic 19 year old still playing with X-Wing pilot helmet) He tells Han that he's Resistance (that one lasts about a minute - Han was not a romantic 19 year old even at 19 :)   In reality, we know that he was 1% of his class, model stormtrooper cadet, personally groomed for promotion by Captain Phasma (; ).  However, I am pretty sure telling Han "Hey, I was 1% of my class, model stormtrooper cadet, groomed for promotion by Captain Phasma"  isn't high on his list of brand management plans.  Far better to pretend to be a lowly "sanitation" worker than top-flight cadet that he really was.  So, my question is - do we have any direct canon evidence proving that the "sanitation" job was real and not a fib to make himself look better to Han/Resistance?  Knowing where trash compactor was isn't direct evidence, though it is circumstantial one. What happens if there is a security problem in a package in the universe repository four years after the 12.04 LTS release; will the package be updated from upstream, patched, or left alone?  It's my understanding that the "5 years of support &amp; security updates" applies only to the core of Ubuntu -- anything in Main repository.  Not for things in the Universe repository.    For a more specific example -- if I install Ruby now, and want to use it for the next several years on 12.04 and it has a security vulnerability; while this might be patched in the upstream (so I could always download the latest from their website and compile it myself or use a PPA), will this upstream fix be migrated into the precise package repositories? What about backports? Asking the position of a person in a sequence How to ask the position(?) of a president (like 10th) of a country, correctly? Every cyclic group with order > 2 has at least 2 distinct generators Every cyclic group with order > 2 has at least 2 distinct generators   Here's what I've got so far:  Either order of our group, $G$, is finite or infinite.  Suppose infinite: then our group is isomorphic to $\mathbb Z$ under addition. This group has two distinct generators, therefore so does $G$.  Suppose finite: Then $G$ is isomorphic to $\mathbb Z_n$ under addition modulo $n$.  We know order of $G$ is $\geqslant 3$. If order of $G$ is odd, both 1 and 2 are generators of $\mathbb Z_n$ under addition modulo $n$, so $G$ has at least two generators.  If order of $G$ is even, then both 1 and some odd number between 1 and $n$ are generators. How do we determine this odd number?  Does this look like I'm on the right track? Windows registry entries for default explorer view How do I get the MAX row with a GROUP BY in LINQ query? Why "grand theft auto", not "grand auto theft"? There is a video game series called "Grand Theft Auto".  According to its :     The name of the series references the term used in the US for motor   vehicle theft.      [...]      Motor vehicle theft or, grand theft auto, is the criminal act of   stealing or attempting to steal a car (or any other motor vehicle).   I always wondered why this term sounds so strange.   Shouldn't it be "grand auto theft" or maybe "grand theft of auto" instead? Are there any other terms with strange words order and/or missing prepositions like this? Does "the same number of people" behave as singular or plural? This hurts my eyes to read it and my ears to say it, but the writer stands by          About the same number of people was awarded bachelor's degrees in 2010 as filed for personal bankruptcy (1.6 million).   Is the subject in this sentence singular or plural? Every convergent sequence in a metric space has a unique limit. For $n$ a positive integer, let us write $\zeta_n = e^\frac{2 \pi i}{n}$, a primitive $n$th root of unity. It is clear that, if $m$ divides $n$, then we have an inclusion of cyclotomic fields $$ \mathbb{Q}(\zeta_m) \subseteq \mathbb{Q}(\zeta_n).$$ On the other hand, these inclusions are not always strict. For example, since $\zeta_3  = \frac{1+i \sqrt{3}}{2}$ and $\zeta_6 = \frac{-1 + i \sqrt{3}}{2}$, we have $$\mathbb{Q}(\zeta_3) = \mathbb{Q}(\zeta_6) = \mathbb{Q}(i\sqrt{3}).$$ Does this sort of thing happen infinitely often, or are there just some coincidences among small numbers? If this continues, is there some way to know when a particular inclusion of cyclotomic fields is strict? How do I get the subscribers of an event? I need to copy the subscribers of one event to another event. Can I get the subscribers of an event (like MyEvent[0] returning a delegate)?  If this is not possible I would use the add accessor to add the delegates to a list. Would that be the best solution?