Quantum probability
Why is the application of probability in QM fundamentally different from application of probability in other areas?
Sum of compact sets Let $A,B$ two non-empty compact subsets of a normed space X. How can we prove that the set $S=A+B=\{a+b : a \in A, b \in B\}$ is compact?  Here's my reasoning:  Let $\Omega = \{\Omega_1, \Omega_2,…\}$ be an open cover of $S$. $\Omega$ induces two open cover $X,Y$ respectively of $A,B$, where   $X_i = \{a \in A : a+b \in \Omega_i~~for~some~b\}$   $Y_i = \{b \in B : a+b \in \Omega_i~~for~some~a\}$  in practice $\Omega_i = X_i + Y_i$.  Now my idea is build a finite subcover this way: consider a finite subcover $X_F = \{X_j : j \in J\}$ where $J$ is a finite set of indices. If $Y_F = \{Y_j : j \in J\}$ is a finite subcover of $B$, then we are done as $\{\Omega_j : j \in J\}$ is a subcover of $\Omega$. Otherwise we can keep adding indexes to set $J$ until $Y_F$ becomes a finite subcover of $B$.   This is not too formal but I don't want to make a simple question unreadable, I think the idea should be clear.   Does this works? Is there a better/easier way to get the same result? Getting two pictures to appear on the same page density of $X^2$ when $X$ has uniform $[-1, 2]$ distribution Emacs: How to use a major mode for non-standard file extension Why does editing posts on SO require a minimum of 6 charaters? I have just recently started editing the post on Stack Overflow.  I found some posts which only required 2-3 character changes like they had correct grammar but some mistakes in spelling.  When I tried to correct the spelling mistakes, and clicked on "edit", it said:  Edits must be at least 6 characters   I don't know why Stack Overflow added this limit. How can I edit only 3-4 characters in a post? How to make files protected? I installed the latest pgAdmin 4 (v2.1) but I found out that (), for the moment, the only way to establish a connection through an SSH tunneling is using another outside process, an  says:  I setup a tunnel as follows: ssh -f dpage(at)hostname(dot)enterprisedb(dot)com -L 5999: hostname.enterprisedb.com:5432 -N  (...) I was running on Mac, but the same procedure should work on Linux. On Windows, there's a tunnelling app in Putty iirc, but I don't know how to use it offhand.  I have found a simple . The connection is established but it seems, when I try to connect through pgAdmin it fails or is refused (using 127.0.0.1:3306 or 127.0.0.1:5432 as the tunnel's destination). Why? I think it would be nice to have a "friends list" on Stack Overflow. This would allow us to be able to follow the questions and answers that are posted by users that we want to watch/monitor.  I suggest it be implemented in the same fashion as DotNetKicks.com; where you can add someone to your "friends list" without them needing to approve you the way that other social networks do it. It should be completely open for us to add anyone to our "friends list" that we like. Canonical Question  I want to do &lt;some really cool thing&gt; with a lightning:datatable, but I can't seem to figure out how to do it. I checked the , but I did not see a way to implement &lt;this really cool feature I need&gt;.  Perhaps I want to provide tooltips, or a pick list, or alter the behavior of the menus, or display images, or show a custom component I created, or define a new row-level click behavior, or alter the keyboard event handlers, etc.  Can I somehow do this? When you are viewing an app in Google Play store, it displays the following : Updated, Size, Installs, Current Version, Requires Android, and Rating.  I am trying to do some research and figure out the initial release / publish dates of different apps. Is there a way to get this information from Google Play, or perhaps a website with this information? Forgotten iOS Restrictions Password/Passcode Error System.CalloutException: Callout from scheduled Apex not supported i have created a schedulable class which has to trigger a batch job. The run method for the batch class will get list of data to process from a webservice callout. Now, i got the exception below. Any suggestions please.     System.CalloutException: Callout from scheduled Apex not supported.   global class scheduledDeltaBatchable implements Schedulable {    global void execute(SchedulableContext sc) {     ID batchprocessid = BatchUpsertSAPCustomerMasterBPSync.run(SAPServices.GetSAPCustomerMasterBPSync('Delta'));    } } SBS 2011 - Is Store.exe High Memory Usage Normal? Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$ I am studying combinatorics and I came across the identity $$\sum\limits_{k=0}^n \binom kp =\binom {n+1}{p+1}.$$ I have read the algebraic proof and it does not appeal to me. Is there an elegant counting trick we can use to arrive at this identity? Is it possible to plot a graph of any shape? I have the table below and i want it to read through columns A-B and then sum the values that match their names in columns C-D.  So that in a column elsewhere of a list of names i have the sum of their values from this table. For example Ed features in both columns with a value of 1 and 3, so would return a value of 4. Struggling to get this to work nicely. My actual table consists of 4 columns names and two sets of 4 columns with numbers.    A       B       C   D Steve   Jeff    4   1 James   Calum   1   1 Alex    Andy    2   1 Peter   Ed      0   3 Owen    Harry   1   2 Jeff    Steve   4   1 James   Calum   1   1 Andy    Alex    2   1 Peter   Owen    0   3 Ed      Harry   1   2 How to programmatically click a button in WPF? What is the longest word you can come up with that the letters are all in alphabetical order? It's Friday again, how about some fun to get us into the weekend?  What is the longest word you can come up with for which all the letters in that word are in alphabetical order?   Rules:   English words only    Can't be a name of a place, person or other proper noun.   if it contains the same letter twice in a row, that does not disqualify it.   No fair looking it up on Google!   Update: One more rule to help you guys out.   The word can be in either ascending or descending alphabetical order. JavaScript for...in vs for Do you think there is a big difference in for...in and for loops? What kind of "for" do you prefer to use and why?  Let's say we have an array of associative arrays:  var myArray = [{'key': 'value'}, {'key': 'value1'}];   So we can iterate:  for (var i = 0; i &lt; myArray.length; i++)   And:  for (var i in myArray)   I don't see a big difference. Are there any performance issues? Processing time/speed for Mosaic to New Raster I have a question on speeding up “Mosaic to New Raster” or finding an alternative.  After completing a suitability analysis we are trying to define movement corridors.  We used a modified CircuitScape that left 4 folders, each containing 1080 raster tiles across our study area.  We now need combine all 1080 rasters in each folder then combine these 4 combined rasters into a final raster which will be analyzed for paths.  I tried a python script that just wouldn’t work so I went on to Model Builder.  It iterates through the grids in the folder, collects the values (raster names), then mosaics all to a new raster.  It has been running for 5 days now and the results window indicates it is working.  I’m hoping it will conclude in the next day or 2.  But, we still have 3 more folders, each with 1080 rasters, that need to be mosaicked.  So….is there a way to speed up Mosaic to New Raster or is there an alternative I could use to produce the final grid?    The cell size is 270 meters, 540 x 540 columns and rows, 1 band, 32 bit floating.