Trouble proving that $\mathbb{R} \approx \textbf{I} $
$\mathbb R$ has the same cardinality of any interval
It is possible to make ls -l output the size field with digits grouped by thousands? If so, how?  For instance:  $ ls -l -rw-rw---- 1 dahl dahl 43,210,052 2012-01-01 21:52 test.py   (Note the commas in the size).  Maybe by modifying the LC_NUMERIC setting inside the locale I'm using (en_US.utf8)?  I'm on Kubuntu 12.04 LTS. Can I vent my dryer into the crawl space without creating mold and moisture problems? We have a crawl space with a combination of sandy and clay soil in it.  The crawl space is about 3' deep.  To eliminate a long dryer vent run, I'd like to vent the dryer directly into the crawl space.  We have vents built into the foundation that I open each spring and close in the fall.  Will this help dissipate the moisture enough to prevent mold? What is so called meta-game in StarCraft 2?    What other games have this meta-game? How long does it take for DNS records to propagate? How is the notation $X\sim N(\mu,\sigma^2)$ read? Is it $X$ follows a normal distribution? Or $X$ is a normal distribution? Or perhaps $X$ is approximately normal..  What if there are several variables that follow (or whatever the words is) the same distribution? How is it written? setting upper and lower limits in rnorm Basically I would like to use on website a "Norasi" font, that was bundled with Ubuntu, but I cannot find any license. Am I allowed to distribute that font through website? What is its license? What does closed form solution usually mean? This is motivated by  and the fact that I have no access to Timothy Chow's paper  indicated there by Qiaochu Yuan.  If an equation $f(x)=0$ has no closed form solution, what does it normally mean? Added: $f$ may depend (and normally does) on parameters.   To me this is equivalent to say that one cannot solve it for $x$ in the sense that there is no elementary expression $g(c_{1},c_{2},\ldots ,c_{p})$ consisting only of a finite number of polynomials, rational functions, roots, exponentials, logarithmic and trigonometric functions, absolute values, integer and fractional parts, such that   $f(g(c_{1},c_{2},\ldots ,c_{p}))=0$. How do I create a file of size 10M, format it with ext3 filesystem and then mount it in /media/fuse?  I tried with  mkfs -t ext3 file   then to mount it  mount -t ext3 file /media/fuse   It didn't work because it said that file wasn't a block device. Can anybody help me? Real definition of "countable set" How to install hp scanjet 200 in Ubuntu 12.04? Unable to scan with hp scan-jet 200. When I type lsusb command in terminal it shows the scanner details.  I opened the simple scan which displays no scanners found, and x sane image scanners also displays the same error. ^x^y unix trick for all instances in last command? One of my favorite Unix tricks is ^x^y, which will take the last command and replace the first instance of "x" with "y". However, I'm wondering if a similar trick works to replace all instances of "x" with "y" in the last command? Why is compactness in logic called compactness? In logic, a semantics is said to be compact iff if every finite subset of a set of sentences has a model, then so to does the entire set.   Most logic texts either don't explain the terminology, or allude to the topological property of compactness. I see an analogy as, given a topological space X and a subset of it S, S is compact iff for every open cover of S, there is a finite subcover of S. But, it doesn't seem strong enough to justify the terminology.   Is there more to the choice of the terminology in logic than this analogy? RECENTLY ON THE ANDROID SITE WE GOT  WRITTEN IN ALL CAPS.  THIS WAS SURPRISING TO ME, SINCE I ASSUMED IT WOULD HAVE BEEN CAUGHT BY THE QUALITY FILTER &mdash; BESIDES BEING INDICATIVE OF OTHER POST QUALITY ISSUES, IT'S AWFUL TO LOOK AT AND REQUIRES A LARGE AMOUNT OF EDITING TO FIX (EVEN IF YOU RUN IT THROUGH TOLOWER() FIRST).  WE ALL KNOW THAT CAPS LOCK IS , BUT STILL: CAN WE BLOCK THESE QUESTIONS?    RICK  RICK  OH MAN THAT STUFF JACOB G  IS COMEDY GOLD  RIIICK     Note to editors: This post looks exactly like it is supposed to look, as an example of a question in all-caps. Please do not replace the uppercase letters with lowercase. For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$  Oh, the exponential of a matrix is: $e^A=\sum_{i=0}^\infty\frac{1}{i!}A^i$    I thought I'd solved the $e^A$ form but I actually did something really silly, now I'm a little stuck.  If $A^k=I$ then $A^{k+1}=A$ and we have a cycle forming, so we will get:  $$\sum^{k-1}_{i=0}\sum^{\infty}_{j=1}\frac{1}{(kj+i)!}A^i$$  (Or something like this form, I don't have paper to hand and just spotted that now)  Is this what the question wants? It doesn't use the 2x2 property.  I believe the answer lies in finding an expression for the inner summation, I can do this for two terms (think of $e+e^{-1}$ all the odd power leave) I could install with an error message "unknown media /ALL". It could not run WPS Office. Why multiple capacitors in parallel? Wondering why you would choose to use smaller capacitors in parallel vs one bigger one.  Here's an example:      Is this a component size and track width choice?  Thanks! My model has a clear plastic (or glass) dome with objects inside.  The objects appear dark.  I've tried the glass shader with color 100% RGB, with very small IOR, and using just a refraction shader.    I know Cycles has problems with caustics, but I just want broad illumination to fall clean through the glass.  The light-to-column path can ignore refraction, but is blocked or tremendously attenuated. The camera-column path needs refraction, and seems to work fine anyway.  This demo image offers all optical paths of interest:   light upon object, seen directly light upon object, seen through glass (looks okay) light through glass onto object, seen directly. This is the shadow on the lit side of the column just below the glass tubing.  I expect full illumination, but there is shadow.  There is some light, but it's diffuse light from the floor. light through glass onto object, seen through glass. This     I did at one point try non-progressive rendering, and find extremely coarse light where there shouldn't be shadow, but this is not a practical way to make nice images. I've even tried cranking up certain sampling settings to many thousands, but still get bad noise though less, at the cost of long render times. I  would like to finish my creations sometime before "Star Trek, the Generation After the Next" becomes real life, if you know what I mean.  The next image is an example. I think Transmission in Sampling was 5000, but not sure.    I'm using Cycles in Blender 2.67 on a quad core Linux machine, 16GB RAM. Machine limits have never been a problem for 3D rendering.  Possibly, I screwed up some setting when I made my startup file, and just need to fix it. OTOH maybe this is just a limitation of path tracing, or of the way Cycles does it. If that's the case, what to real-world Blender artists do when they need to produce images on a budget and schedule?  What is the practical real-world fix? "Stack Overflow" showing up on hamburger menu for all sites to link to /questions Why does it say "Stack Overflow" instead of the site name? In Fringe's season 1, the episode  (1x13) shows how  travels on VertusAir flight 718. We witness how he develops some strange symptoms, withdraws into a lavatory and transforms into a porcupine-like monster.  At the end of season 3, Peter "switches" the timeline (changing the past and making the present continue in a different timeline henceforth) from blue- to orange-verse. Various statements throughout the 4th season indicate time (the date) was not reset; Olivia and Walter have been working on Fringe cases for some three years etc. - hence it is safe to say that season 4 plays 3 years after season 1.  Then, in the episode  (4x16), the events from 1x13 happen again, up to the point of Bowman's transformation, which this time doesn't happen (not aboard the plane, anyway). As far as I can tell, great care was taken to exactly recreate the events from the season 1 episode, including hiring the same actors to play the flight attendants once again ( and ), so obviously this is supposed to be the same event with slight changes.  Peter, as well as Olivia - who is in the process of regaining her memories from the blue-verse -, remember the events from 1x13 and note the difference that Bowman's transformation happened later this time, implying that in the orange-verse, everything related to flight 718 played out the same way, except for the small difference that the transformation happened a bit later.  BUT ... all of this happened 3 years later!! Is there any explanation for this?  How unlikely is it that in the orange-verse timeline, Marshall Bowman is on the very same flight with the very same flight attendants 3 years after the same would have happened in the blue-verse? Mind you, this is not a "small change" in the course of events while mostly everything else stays the same.  So, why did Peter and Olivia realize the transformation happened a tad later in the orange-verse timeline, but were not baffled by the fact that essentially the same events as in the blue-verse happened, but three years later?  EDIT: Not only the flight and the flight attendants were the same in both episodes. The passenger next to Bowman was the same, an elderly lady played by  both times, as well. Moreover, the transcripts of  and  reveal that the dialogue between Bowman, the passenger next to him, and the cabin crew is the same down to the lines of text until the moment of transformation.  Interestingly, the announcement by the captain in the beginning seems to be different - starting the inflight movie + selling headsets vs. circling before beginning the final descent + selling snacks. On the other hand, this could be presumed to be a slight retcon, as in 4x16, it was crucial for the plot that the plane would be close to landing, and starting the inflight movie would not make much sense right before landing.