Why does the statement if ( !condition ) { console.log(condition) } display true
What is wrong with my date regex?
The problem statement is: for $a,b$ coprime, prove that there exists positive integers $x,y$ such that $ax-by=1$.  The question is form Arthur Egnels' problem solving text, and from the chapter on the pigeonhole principle.    My question: His proof begins by generating a list $a,\ldots,a(b-1)$, where he then points out that each element in this list(which proceeds sequentially) doesn't have remainder $0\pmod{b}$.  He then shows that we arrive at a contradiction if we assume that we also don't get remainder $1$ in this list $\bmod b$.  To show the contradiction in this last statement, he first states that we would have positive integers $p,q $ where $ 0&lt;p&lt;q&lt;b$ so that $pa\equiv qa \pmod{b}$.  He then goes on to point out that since we $a$ and $b$ are coprime, we then have that $b| q-p$.  I understand the last part here, but don't see why we get $pa\equiv qa \pmod{b}$.  Thanks in advance Portrait for phone, landscape for Tablet (Android-Layout) How to create a Windows 7 installation USB from OS X? I'm trying to create a Windows 7 installation USB (for use on a PC) from OS X.  I've tried following these instructions from a :   Insert the USB flash drive and run the command diskutil list to find out the disk name, we'll use /dev/disk1 as an example Now unmount the disk using diskutil unmountDisk /dev/disk1 dd if=/path/to/Win7.iso of=/dev/disk1 bs=8192   But the instructions don't work. When I insert the created USB drive into my PC and try to boot from it, I get this message:     Reboot and Select proper Boot device or Insert Boot Media in selected Boot device and press a key   What am I missing? Difference between information and knowledge? As far as I think projection of data unto subject mind is information for the subject whereas indentation or impressions accumulated owing to projection of data unto subject mind is knowledge for the subject. I want to know am I right? Or can someone provide a more rigorous answer! Is "The empty set is a subset of any set" a convention? Recently I learned that for any set A, we have $\varnothing\subset A$.  I found some explanation of why it holds.     $\varnothing\subset A$ means "for every object $x$, if $x$ belongs to the empty set, then $x$ also belongs to the set A". This is a vacuous truth, because the antecedent ($x$ belongs to the empty set) could never be true, so the conclusion always holds ($x$ also belongs to the set A). So $\varnothing\subset A$ holds.   What confused me was that, the following expression was also a vacuous truth.     For every object  $x$, if $x$ belongs to the empty set, then $x$ doesn't belong to the set A.   According to the definition of the vacuous truth, the conclusion ($x$ doesn't belong to the set A) holds, so $\varnothing\not\subset A$ would be true, too.  Which one is correct? Or is it just a convention to let $\varnothing\subset A$? Is there a word that contains all the vowels? "Jealousy" contains most of the vowels but lacks 'i'. Is there a word in the English language that contains every vowel (and preferably 'y')? How can I efficiently check the originality of my work? I have a 2 year old son and another baby on the way. I just recently found out I'm pregnant but not sure how far just yet. My son rammed into my stomach like he is always doing but this time it made me start having small pains in my stomach. I rushed to the bathroom to make sure there wasn't any bleeding.  I'm concerned his rough play could hurt the fetus if it continues. How should I put a stop to it? What were the rules for capitalising nouns in the 17th and 18th centuries? It seems to have been common practice in the 17th and 18th centuries in English-language sources to capitalise the first letters of nouns, as in  At which Time he prov'd himself the Noah's Dove, that finding himself no Rest anywhere, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his mouth. —  (1685)  Most original sources I can find on the web have used modern rules for capitalisation, so I have a few questions:  Was the practice used for all nouns (Note mouth isn't capitalised in my quotation above.)? When did this practice begin? When and why did it end? I just bought an Xbox 360 game with wrong region. What should I do? I just bought a  game (Forza 4) for my Xbox 360 (bought in the US). When I tried to play the game, it wouldn't load because of region issue. Is there a legal way to solve this (no crack)? How can I make a bash script executable by double clicking just like .exe files in Windows? I tried , but there are two consequences:   the terminal twinkles, disappears, and nothing is done. you must specify to run in terminal in order to work.   I have a script that installs tomcat on an offline PC, including all dependencies of tomcat in the script. I need to make the script work on double clicking like windows since most who use the script will not be familiar with Ubuntu.  Forget the above explanation. I want to make a script that can be run by double-clicking on it, without using the terminal. Anybody knows how? Prove the inequality $n! \geq 2^n$ by induction I'm having difficulty solving an exercise in my course.  The question is:      Prove that $n!\geq 2^n$.   We have to do this by induction. I started like this:   The lowest natural number where the assumption is correct is $4$ as: $4! \geq 2^4 \iff 24 \ge 16$. The assumption is: $n! \ge 2^n$.   Now proof for $(n+1)$ which brings me to: $(n+1)! \ge 2^{(n+1)}$  I think I can rewrite it somehow like this:  $$ {(n+1)} \times {n!}  \stackrel{\text{(definition of factorial)}}{\ge} 2^n \times 2 $$  $$ (n+1) \times 2^n \ge 2^n \times 2 $$  Then I think I can eliminate the $2^n$ and have something like this: $n+1 \ge 2$, or $n \ge 1$.  But I think I'm wrong here some where and was hoping somebody has some advice on this. How can I prove the above assumption?  Any help would be appreciated, kind regards. Scientists have found very bright source of light which they call  and the are found to be . So these black holes are so massive that they cannot be formed by a supernova. So how are these formed? As per title, I wish to know if I can, after a successful 32bit setup and consequent software installations, update to a 64bit version.  I know how to partition (actually one of the solutions is to set /, /etc, /home, /var/www, and /opt as separate partitions) and I know that a clean install is way better than a dirty one, yet I would like to know if/how it's possible to do that. How to use a C++ string in a structure when malloc()-ing the same structure? Take the square $[0,1]^2$ we take $n$ random lines through the square. You can choose random lines by choosing a point on one of the sides of the squares and randomly choosing a different point on any of the other three sides and then drawing a line connecting them.   What is the probability that after $n$ of these random lines the largest region is greater than or equal to $0.5$?  Any tips or cases help, thanks. How to calculate $5^{3^{1000}}\bmod 101$? I can seem to run scripts (.sh) with and without them being set as executable. So where exactly this matters? I deleted the "/etc/passwd" file and cannot log in I was trying to change my username and also my home directory (/home/username) and my system started to crash. I deleted the passwd file but I had a backup named passwd_bkp. I tried to rename this passwd_bkp as passwd and it did not work. No commands were being executed... I was in a terminal window.   I restarted my system and now I cannot log in. GRUB gives two options: Linux and recovery mode.   I tried to open a sessions as root but it says the filesystem is corrupted. I cannot access my files.  Did I lose all my files? Changing footnote symbols