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How is it possible that quantum phenomenons (e.g. superposition) are possible when all quantum particles are being constantly observed? I don't understand how quantum mechanics (and therefore also quantum computers) can work  given that while we work with quantum states, particles that this quantum state consist of cannot be observed, which is the most fundamental requirement.  If I am not mistaken, by "observed" we mean interaction with any other particle (photon, gluon, electron or whatever else). So my very important questions:   Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse? Aren't all particles in the universe interacting with Higgs field and gravitons etc? Why doesn't that cause every quantum state to collapse?   I feel there is something very fundamental in quantum mechanics that I am not aware of, hence I would be very pleased to have these questions answered. I have from Exercise 1 pg 33 - "Algebra - T. W. Hungerford" following:      Question to proof: Show by example that the first conclusione may be false if $G,\, H$ are monoids that are not group.   I thinked:     Proof: let be for example two monoids $(G:=\{\emptyset\}, \bot)$ and $(H:=\{\emptyset, \{\emptyset\}\}, \top)$ with: $$\begin{array}{c|c} \bot &amp; \emptyset \\ \hline \emptyset &amp; \emptyset \end{array} \, \, \, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \, \begin{array}{c|cc} \top &amp; \emptyset &amp; \{\emptyset\}\\ \hline \emptyset &amp; \emptyset &amp; \emptyset \\ \{\emptyset\} &amp; \emptyset &amp; \{\emptyset\} \end{array}$$ $G$ with $e_G:=\emptyset$ like neutral element and $H$ with $e_H:=\{\emptyset\}$ like neutral element. Let be $f$ a function from $G$ to $H$ with $\emptyset \mapsto \emptyset$ (namely $x \mapsto x$), the function is Homomorphismus in fact $$ \begin{align} {\color{Red}f}{\color{Red}(}{\color{Red}x}{ \color{Red}\bot }{\color{Red}y}{\color{Red})}=&amp;f( \emptyset \bot \emptyset)= {\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}= \emptyset \\ {\color{Red}f}{\color{Red}(}{\color{Red}x}{\color{Red})} {\color{Red}\top} {\color{Red}f}{\color{Red}(}{\color{Red}y}{\color{Red})}=&amp;f(\emptyset) \top f(\emptyset)= \emptyset \top \emptyset= \emptyset \\ &amp;\text{with }x,y \in G \end{align}$$ but it means that $$ \begin{align} f(e_G)&amp;\neq e_H \\f(e_G)={\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}=\emptyset &amp;\neq \{\emptyset\}= e_H \end{align}$$ Therefore $f$ ist Semigroup-Hom but not Monoid-Hom...   Is it correct? Galois extension is (not) transitive Let $ K/ L /F $ be fields. If $K / L$ is Galois and $ L / F $ is Galois, then $ K / F$ is Galois. We mentioned this very quickly in today's class without justifying. But I have trouble seeing this. Any help is appreciated.  Our definition for $ K / F$ being Galois is the $F$-automorphism group $G = G( K / F) : = \{ \sigma \in aut (G) : \sigma_F = id_F \}$ fixes only $F$, i.e. $ \{ x \in K : \sigma (x) = x \text { for all } \sigma \in G  \} = F$.  But we also showed that $ K /F$ is Galois if and only if $ K/F$ is normal and separable. Regular expression to match non-ASCII characters? What is the easiest way to match non-ASCII characters in a regex? I would like to match all words individually in an input string, but the language may not be English, so I will need to match things like ü, ö, ß, and ñ. Also, this is in Javascript/jQuery, so any solution will need to apply to that. For most OpenID options, it doesn't much matter if you pick the "Sign up" versus the "Log in" tab on the sign in page.  Whether you have an account on the site or not, it just does the right thing. Not so if you are using the Stack Exchange OpenID service:    (Bonus bug: the reCAPTCHA box is a bit too wide for the expanded "Sign up using Stack Exchange" container.)  Since we already have collected an email and password (well, two copies of the password), could we not check to see if they match and automagically log the user into their SE OpenID?  If not, the error needs to be reworded somehow to explain that while the email might have been used to create a Stack Exchange OpenID, that doesn't mean they can't log in with that OpenID to create an account.  Counterintuitively, they need to use the  even if they've never had an account there before.  The  link adds to the confusion since it sends an email that leads off with:     Someone requested an account recovery on The Workplace Stack Exchange for jericson@stackexchange.com, but we don't have an account on this site that matches this email address.   (For people with accounts on other sites and/or Stack Exchange OpenIDs, this paragraph is followed by other instructions that would probably work if followed. By that time I imagine many users are at wit's end.)  To simplify: If a user already has a Stack Exchange OpenID (likely because they have an account on another site) they should be able to use the  to sign up for an account or there should be clear instructions on what to do next if they fail. Best way to do multi-row insert in Oracle? What are the minimum requirements to run Windows 10? I am looking to upgrade my system to Windows 10 RTM, but I'm afraid of losing performance.  I researched on the site but found details (maybe I have not sought duty) on the hardware minimum.  What are the minimum and recommended requirements for running Windows 10 RTM? You may have encountered a situation in which Mac changes the order of desktops based on some events like alerts on a program or a web page in browser. How could I disable this logical change? Note: I'm using El Capitan, but I had this problem since Mavericks. Bash-like, non-rotating filename tab completion with PowerShell Under Windows, using PowerShell, is it possible to make the filename suggestion (using the Tab key) work like with bash under Linux?  Let's assume a directory contains 3 directories: example1, example and examination.  On Windows (by default), if you type cd ex and Tab, it will auto-suggest cd .\examination. Subsequent uses of Tab will rotate the suggestion between example1, example and examination.  Using bash (typically under Linux), if you type cd ex and Tab, it will auto-complete until the character where the filenames start to differ: cd exam. Another use of Tab then suggests which directories are available:  $ cd exam examination/ example1/    example2/   Then, if you type p and Tab, it will auto-complete to example, and so on (here, offering a choice between example1 and example2).  Is there a way to make the filename suggestion work in a tree-like search like this, instead of rotating through the names?  (I'm mainly interested in file names. Bash can also refine this selection based on the file type, for example only directories for cd, which would be good, but having the file name selection itself would be enough.) Homeomorphism that maps given points to given points I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ? Is it Possible to Disable Feed and Topics for an Object Completely at Profile Level / Page LayOuts What is the quickest way to send some text from desktop\laptop to iPhone? I usually send emails to myself, but I wonder if there is a better way to share something quickly from my PC\laptop to iPhone. How to lazy load images in ListView in Android I am using a ListView to display some images and captions associated with those images. I am getting the images from the Internet. Is there a way to lazy load images so while the text displays, the UI is not blocked and images are displayed as they are downloaded?   The total number of images is not fixed. How to show  that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal? Is it possible to find the cardinality of $\mathbb{Z}[i]/I$ as well?  I know how to show that it is an integral domain, because that follows very quickly. Show that $13$ divides $2^{70} + 3^{70}$.   My main problem here is trying to figure out how to separate the two elements in the sum, and then use Fermat's little theorem. So how can I separate the two?  Thanks! Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers. I think i have proved that any number of the form $2^n$ can't be written as the sum of k consecutive positive integers, but i would be grateful if i could have some clarification as to whether this is a correct and valid proof or not.  Let $g=x+(x+1)+(x+2)+(x+3)+...+(x+(k-1))$, hence g is the sum of k consecutive positive integers.  $g=kx+\sum_{d=1}^{k-1}d$  Hence, $g=kx+\frac{k(k-1)}{2}$  Rearranging for x we find, $x=\frac{g}{k}-\frac{(k-1)}{2}$  So, for certain values of $k$, we can be sure that a positive integer value of $x$ can be found, and hence $g$ can be written as the sum of $k$ consecutive positive integers.There are two cases for $k$ to considor:  Case 1)  $k$ is odd. If $x$ exists, it must be the case $k$ | $g$, as for odd values of $k$, $\frac{(k-1)}{2}$ will alwyas be an integer, and hence $x$ will.  Case 2)  $k$ is even. $k$ does not divide $g$, but $\frac{g}{k}$ must be a multiple of $\frac{1}{2}$, and hence equals $\frac{h}{2}$, for some odd $h$.  Letting $j=2^n$, assume that we can write $j$ as the sum of $k$ consecutive positive integers.  If $k$ is odd, then if a $k$ exists, it must divide $j$, by Case 1. But, $j$ has no odd factors as it is a power of two, hence $k$ could not be odd.  If $k$ is even, by Case 2 it mut be the case $k$ does not divide $j$. Also, $\frac{j}{k}=\frac{h}{2}$, for some odd $h$.  But, this implies $2j$ has an odd factor, $h$. but, as $2j$ is a power of $2$, it can't have odd factors. So, $k$ can't be odd.  Hence, $k$ is neither odd or even, and this is a contradiction to our assumption. Hence no $x$ exists, and hence and number of the form $2^n$ can't be written as the sum of $k$ consecutive positive integers.  Any feedback on this proof would be appreciated. Changing unusual foreign currencies in London I've just returned from several unusual countries in Asia, and annoyingly despite being told I'd have no problem, I'm unable to find anyone in London to change back to pounds.  I've tried Travelex in Heathrow, a currency exchange place, and the post office.  The currencies include cash from: Mongolia, Kyrgyzstan, Kazakhstan and Uzbekistan.  Most of the responses when shown the money is to the tone of "What the hell currency is this?" which doesn't fill me with confidence.  Any suggestions welcomed for places that may change this. Otherwise I may need to go back next year ;) "wait on" or "wait for"? Officials are waiting on autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin.   I am curious about the preposition on in the sentence, because I usually say "wait for" instead of "wait on". Does it still have the same meaning if I change on to for? Just as follows:     Officials are waiting for autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin. Allowing line break at ',' in inline math mode? In the inline math mode ($...$), if the formula is too long, LaTeX will try to break it on operators, e.g.  very long text followed by a very long equation like $a+b+c+d+e+f+g+h+i+j+k+l$ etc   may be rendered as  very long text followed by a very long equation like a+b+c+d+e+f+g+h+i+ j+k+l etc   However, the break won't happen if they are separated by commas, e.g.  very long text followed by a very long equation like $a,b,c,d,e,f,g,h,i,j,k,l$ etc   will overflow the page like  very long text followed by a very long equation like a,b,c,d,e,f,g,h,i,j,k,l etc   How to make LaTeX able to insert line breaks after a comma too?