What is time complexity of nested loop where inner loop is j < i?
Time complexity of nested for-loop
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$ Using only rules of natural deduction, I am trying to prove that $$p \implies q \vdash \lnot p \lor q$$ but am having a lot of difficulty. I was able to prove the other direction.   Could anyone show me or point me to the right direction? Are the XBLA and PC versions of Minecraft compatible? Trying to identify a short sci-fi story about a human that is "resurrected" by malignant aliens How to choose a lens for my first DSLR? I am considering buying my first DSLR.  How do I know whether I need a 18-200 lens, 17-85, or 18-55? Or something else? Assume $f:\mathbb R\rightarrow  {\mathbb R} $ is Lebesgue integrable, prove $\sum_{n\in\mathbb N } f(x+n)$ converges for almost everywhere x. This is a question discussed with friends. Thanks Korean characters scrambled [XeLaTeX; Noto Sans Korean]? I was trying to find a font which has obsolete jamo and the right combining behaviour. Yesterday I found out about , which seems to have both of these. However, when I use it in XeTeX, I get some seemingly-arbitrary hanja (or blank spaces) instead of the expected characters.  (I’m guessing the composing behaviour will fix itself when the right characters are selected. And yes, I know that Code2000 is working perfectly in this example, but unfortunately it is the ugliest font in the world. :p)  MWE:  \documentclass{article} \usepackage{fontspec}  % 1. precomposed: U+BB47 % 2. separate jamo: U+1106, U+116E, U+11BA % 3. obsolete [separate jamo]: U+113B, U+119F, U+11EB \newcommand\test[1]{#1 &amp; {\fontspec{#1}{뭇; 뭇; ᄻᆟᇫ}} \\}  \begin{document}  \begin{tabular}{rl} \test{Arial Unicode MS} \test{Batang} \test{Code2000} \test{Gulim} \test{GungSeo} \test{HeadLineA} \test{Nanum Brush Script} \test{Nanum Myeongjo} \test{Nanum Pen Script} \test{Noto Sans Korean} \test{PCMyungjo} \test{PilGi} \test{Adobe Gothic Std} \test{Adobe Myungjo Std} \test{Apple SD Gothic Neo} \test{AppleGothic} \test{AppleMyungjo} \end{tabular}  \end{document} "None" as plural indefinite pronoun In my grammar book (English Grammar, HarperCollins Publishers), I read that none is occasionally treated as plural, but it is usually regarded as singular. Can you give me an example of sentence where none is used as plural pronoun? Why don't we treat rubbish the same as spam? How Do Dementors Communicate with Wizards? Is there a list of Windows special directories/shortcuts (like %TEMP%)? I'm looking for a reference list of shortcuts like %TEMP%.  When I'm using Windows+R or Windows Explorer and type %temp%, the Windows Explorer takes me to the Temp directory. Are there more of these shortcuts?  UPDATE: . Prove that the unit circle, $S^1:=\{(x,y)\in \mathbb{R}^2: x^2+y^2=1\}$, Is a one-dimensional manifold Taking advantage of one-time pad key reuse? Suppose Alice wants to send encryptions (under a one-time pad) of $m_1$ and $m_2$ to Bob over a public channel.  Alice and Bob have a shared key $k$; however, both messages are the same length as the key $k$.  Since Alice is extraordinary lazy (and doesn't know about stream ciphers), she decides to just reuse the key.  Alice sends ciphertexts $c_1 = m_1 \oplus k$ and $c_2 = m_2 \oplus k$ to Bob through a public channel.  Unfortunately, Eve intercepts both of these ciphertexts and calculates $c_1 \oplus c_2 = m_1 \oplus m_2$.     What can Eve do with $m_1 \oplus m_2$?     Intuitively, it makes sense that Alice and Bob would not want $m_1 \oplus m_2$ to fall into Eve's hands, but how exactly should Eve continue with her attack? Euclidean geometry in non-inertial frame How to fix apt: Signature by key uses weak digest algorithm (SHA1)? I started setting up by adding repositories and then went to run a sudo apt-get update again before I started installing other software, and I get the Signature key lines and it stops. So it essentially won't let me update any packages now.  d@EliteBook:~/Downloads$ sudo apt-get update Ign:1 http://dl.google.com/linux/chrome/deb stable InRelease Hit:2 http://dl.google.com/linux/chrome/deb stable Release                      Hit:4 http://security.ubuntu.com/ubuntu xenial-security InRelease               Get:5 http://ca.archive.ubuntu.com/ubuntu xenial InRelease [247 kB] Hit:6 http://ca.archive.ubuntu.com/ubuntu xenial-updates InRelease Hit:7 http://ca.archive.ubuntu.com/ubuntu xenial-backports InRelease Fetched 247 kB in 0s (256 kB/s)                    Reading package lists... Done W: http://dl.google.com/linux/chrome/deb/dists/stable/Release.gpg: Signature by  key 4CCA1EAF950CEE4AB83976DCA040830F7FAC5991 uses weak digest algorithm (SHA1) d@EliteBook:~/Downloads$   I've never seen this before whenever I setup and start installing things in Ubuntu. Is there something else I can do? How to use mysql JOIN without ON condition? How to get the Input and output in a terminal to a text file? I want to create a text file which will add each command I am going to run on the terminal as a new line entry in the text file. i.e., I need to keep a record of what are the things I'm doing in the terminal. Further if I can keep a record of outputs I'm getting in the terminal, along with the inputs in the terminal, as a text file, it will be much better.   Each time I forget a command I have to search again in the Internet for the command.  Can I can make a file like above? Create keyboard shortcuts for touch bar's functions I have broken the touch bar in my MacBook Pro 13". Only the ESC key keeps working.  Replacing the touch bar may be expensive so I'd like to know if it is possible to replace its functions with keyboard shortcuts.  The functions I am highly interested in are:   volume screen backlight keyboard backlight Theorem numbering I tried Office 2013, but now wish to uninstall it. I tried to uninstall it but it always hangs at step  2 out of 4. It uses no CPU and no disk activity. So basically it's just idle.   Does anyone have a solution to this problem? My objects are semi-transparent, and not one behind the other in the compositor