Does posting questions on weekends reduce the chance of getting an answer?
What is the best time to ask questions?
Change .jpg quality of terminal screenshots Why is it called an “Indian file”? why is my careers profile reputation lower than my actual repuation? How do I prove that $m(TE)=\left|\det(T)\right|m(E)$? Let $m$ be the $n$-dimensional Lebesgue measure and $T$ be a linear operator on $\mathbb{R}^n$. Let $\Sigma$ be the sigma-algebra of Lebesgue measurable sets. How do prove that (1) $\forall E\in\Sigma, T(E)\in \Sigma$ and $m(T(E))=\left|\det(T)\right|m(E)|$? Since the $\sigma$-algebra of Lebesgue measurable sets is strictly larger than the borel algebra, I think it cannot be proven by showing that $T$ is continuous. How do I prove this formally? I have a script from UC Davis and every thing is proven precisely here, except for one lemma which is critical for rest proofs in the script. That is,  Define $\mathbb{B}=\big\{\prod_{i=1}^n [a_i,b_i) : a_i,b_i\in\mathbb{R}\big\}$. Let $T$ be a unitary operator on $\mathbb{R}^n$. Let $A\in \mathbb{B}$ and $\{A_k\}_{1≦k≦m}$ be a finite disjoint sequence such that $\bigcup_{1≦k≦m} A_k \subset T(A)$. Then $\sum_{1≦k≦m} m(A_k) ≦ m(A)$.  It's written in the script: &quot;This result is geometrically obvious, but a formal proof seems to require a fuller discussion of the volume function on elementary geometrical sets, which is included in the theory of valuation in convex geometry. We omit the details&quot; It's okay to me to go through full discussion of volume function if that is precise. If it cannot be proven another easier way(so I can prove it in a day), please recommend me a &quot;convex geometry&quot; text which explains this. Books automatically deletes my books when offline, and when there is enough space on device Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$? I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. In Minecraft, is there any way to make tools indestructible (without using mods)? I want to make some tools indestructible (for an adventure map). Is it possible to do this using enchantments (or a command of some kind?) Square root of 1 is (not) -1 Possible Duplicate:          I was thinking on the following line of thoughts: $1 =  \sqrt{1} = \sqrt{-1 \cdot -1} = \sqrt{-1} \cdot \sqrt{-1} = i^2 = -1$  Of course this is not true, but I was wondering which step in this 'line of thoughts' is forbidden to make?   Thanks for the explanation. Error in Obj-C : Expected identifier or '(' Is Borden's true identity real, or another ruse? Towards the end of , it's revealed that Borden accomplishes his Transported Man trick by using his twin brother, Fallon, as a double. It then becomes clear that he has been doing this in his personal life as well as on stage - each brother leads 'half a life', sometimes appearing as Borden and sometimes as Fallon. This is how he completes the illusion: one Borden goes into the first door, the other Borden emerges from the second door a moment later. Angier doesn't know how Borden does the trick, and doesn't believe Borden uses a double despite being told as much by Cutter. He follows what he believes to be a clue in Borden's notebook and travels to Colorado to meet Nikola Tesla, who Angier believes can build a machine that can help him perform the trick. Angier believes that Tesla built a similar machine for Borden. However, the final pages of the notebook reveal that Tesla was merely a red herring, designed to get Angier out of Borden's way for a long time. Tesla, it turns out, had never built such a machine before. At this point, Tesla agrees to build Angier's machine anyway. Instead of building a machine that transports matter, he builds one that duplicates it. Angier uses this machine in his act, but in order to avoid having to deal with multiple clones (the &quot;prestige materials&quot;), one of them must die as part of the act. This all makes sense, so far, but I find it hard to believe that Borden's use of the word 'Tesla' as the key to his cipher is random. It's too coincidental that he sends Angier on a wild goose chase, but Angier returns with a working machine. A film that is otherwise so tightly plotted shouldn't rely on coincidence to move the narrative forward, so there must be something else going on. Is it possible that Borden cloned himself using Tesla's machine? Installing QGIS on Ubuntu 14.04? Following the QGIS installation guide I have tried both UbuntuGIS and QGIS stable, but both fail with the error message:  The following packages have unmet dependencies:  python-qgis : Depends: python-qgis-common (= 2.6.1.1+trusty1) but it is not going to be installed             Depends: libqgispython2.6.1 but it is not going to be installed            Depends: libqgis-analysis2.6.1 but it is not going to be installed            Depends: libqgis-core2.6.1 but it is not going to be installed            Depends: libqgis-gui2.6.1 but it is not going to be installed            Depends: libqgis-networkanalysis2.6.1 but it is not going to be installed   qgis : Depends: libgdal1h (>= 1.8.0) but it is not going to be installed      Depends: libqgis-analysis2.6.1 but it is not going to be installed     Depends: libqgis-core2.6.1 but it is not going to be installed     Depends: libqgis-gui2.6.1 but it is not going to be installed     Depends: libqgis-networkanalysis2.6.1 but it is not going to be installed     Depends: qgis-providers (= 2.6.1.1+trusty1) but it is not going to be installed     Recommends: qgis-plugin-grass but it is not going to be installed     Recommends: qgis-plugin-globe but it is not going to be installed   E: Unable to correct problems, you have held broken packages.    I had QGISv.2.4 running on my machine with Ubuntu 12.04. After upgrading to Ubuntu 14.04 I was getting error message that pyqgis could not be loaded.  So I uninstalled QGIS using the Ubuntu Software Center and also run  sudo apt-get purge qgis   After that I tried to install the latest version of QGIS Debian Stable and UbuntuGIS unstable but getting the error messages described above.  The weird thing is that neither Ubuntu Software Center nor apt-get list have QGIS listed as installed, but if I run a search for qgis on my file system qgis and all its dependencies are still there. That's why I getting told to have broken packages. JavaScript object: access variable property by name as string Suppose I have BaseClass with public methods A and B, and I create DerivedClass through inheritance.  e.g.  public DerivedClass : BaseClass {}   Now I want to develop a method C in DerivedClass that uses A and B.  Is there a way I can override methods A and B to be private in DerivedClass so that only method C is exposed to someone who wants to use my DerivedClass? Simple past or past perfect with "by" and years What is the difference between      He became a star by 1990's.     He had become a star by 1990's.    Is the first sentence correct? If yes, then please tell me the difference between the two. How to measure time taken by a function to execute I watched a video on  and read a few  which say that human beings see 3D because we have two eyes. But does that mean when I close one of my eyes, I should see 2D? It doesn't happen so. Why am i still able to be understand depth? Would a person with one eye not be able to perceive depths? Service not avaliable Unity3d error in Kubuntu I'm trying to use  in Kubuntu, but I'm getting this error:  Service not avaliable, please try again later.   I've found :  Certain systems may experience "Service unavailable" errors when trying to log in. WORKAROUND: Launch Unity with LD_PRELOAD=/usr/lib/libresolv.so.2 /path/to/Unity (check the path to your local libresolv)   I've checked the path of libresolv.so.2 in my computer. I found it under /lib32/libresolv.so.2 and under /libx32/libresolv.so.2. (Don't know what the difference is).  When I run:  LD_PRELOAD=/lib32/libresolv.so.2 /opt/Unity/Editor/Unity   I get:  ERROR: ld.so: object '/lib32/libresolv.so.2' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS32): ignored.   and when I run:   LD_PRELOAD=/libx32/libresolv.so.2 /opt/Unity/Editor/Unity   I get:   ERROR: ld.so: object '/libx32/libresolv.so.2' from LD_PRELOAD cannot be preloaded (cannot open shared object file): ignored.   With both commands I also get this:  /opt/Unity/Editor/Unity: /opt/Unity/Editor/Data/Tools/libgpg-error.so.0: no version information available (required by /lib/x86_64-linux-gnu/libgcrypt.so.20)   Any suggestion? I have just started learning Japanese Mahjong and I am a bit lost as to why this hand failed.  I did several pons and chis over the course of a hand, having a total of three open melds (one set and two sequences).  Apart from these I had an incomplete bamboo sequence of II and III as well as a pair of dragons, therefore I was on a single wait for I or IV bamboo stick tile. When the IV tile appeared in one of the discards of other players, I was given a choice to do another chi and declare another open meld, but I couldn't win with a ron. Why was that?  Am I wrong that winning by ron guarantees a single needed yaku to win a hand, just like Closed Tsumo does?  After declaring the chi I was offered with, my hand was left with a single pair of tiles, one of which I had to discard.  Eventually the round finished with a draw.  Why couldn't I win this hand with a ron on the IV bamboo tile, and why was I given only the choice of chi instead? Why do I have so many .Xauthority.* files in my home directory? fitting a smaller range when we bought our house, it had a very used 40" gas range. now that range has died. replacing with a new 40" range is very pricey ($2k+), and our cooking needs don't justify the size anyhow.  i'm looking for ideas on how to fit a smaller range. i would imagine that extending the counter top and cabinets would be a pretty extensive change. we've found we can get a 36" range for around 1/2 the cost. would it be feasible to add some sort of storage along side the smaller range to fill in the space?  thanks. i know this is an open-ended question with no specific answer, i'm just looking for ideas.