So I was asked a question by someone that "if everything in the universe is expanding, then the lens we use to look at stellar objects is expanding as well, meaning we shouldn't be able to tell the difference at all".  I replied with "local forces overpower expanding forces, hence the lens doesn't change size at all, whereas at cosmic scales, local forces are too weak so things move apart. In other words, the lens doesn't change size, the question is false, the universe is expanding"  He replied with "the lens DOES change size, just at a different rate than stellar objects are moving apart from each other, hence we know the universe is expanding"  So, what's the actual answer?  I also looked into a similar question:   But here, OP stated in his question (after receiving an answer) that:     The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me.   This is exactly what I mean to ask. Is the expansion of space a "force" that can be overcome, or not? Unfortunately, nobody has addressed that part of the question in that thread, hence I'm asking here.
I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me.
Are there any rules related to the creation of a ?   I am aware of the creation method for the amulet. But I'm asking about creating the actual construct. If I multiclass into 2 or more spellcasting classes, how do I determine my known/prepared spells? If $a^{n}-1$ is prime then $a=2$ and $n$ is prime? I was doing some basic Number Theory problems and came across this problem :     Show that if $a$ and $n$ are positive integers with $n\gt 1$ and $a^{n} - 1$ is prime, then $a = 2$ and $n$ is prime   My Solution : (Sloppy)        $a^{n}-1$ = $(a-1)$ . $(a^{n-1} + a^{n-2} + ... + a + 1)$   This means that $(a-1)$ | $(a^{n}-1)$    But $(a^{n}-1)$ is prime   So , $(a-1)$ = 1 $\Rightarrow$ $a = 2$   Now , let $n$ be composite   $n = kl$ , where $1 \lt k \lt n$ and $1 \lt l \lt n$   Now , $a^{kl}-1$ = $(a^{k}-1)$ . $(a^{k.{(l-1)}} + a^{k.{(l-2)}} + ... + a^k + 1)$   This means that $2^{n} -1$ is composite    Hence , we have achieved a contradiction      My Question : Am I correct ? I've created a map system for a game that runs on the principle of drawing the picture of the map from tiles. There are many reasons for this which I won't go into here but if you really want to know then I'm sure you can find out how to contact me ;)  I have  so you can see exactly where the problem lies and the source. The issue is the line between the top 2 tiles and the bottom 2 tiles, I can't figure out why it's gone like this and any help would be appreciated.  In the source is a marker called "stackoverflow", if you search for "stackoverflow" when viewing source then it should take you to the table in question.  I have also uploaded an . Citation: refer to author or paper? What is the British English way of referring to a source in-text.  Is it plural because there are two authors, like this:         X and Y (2011) describe ...   Or is it singular because you are referring to a singular source, like this:     X and Y (2011) describes...   So what I am asking is whether you refer to the source or to the authors? How do I compare two string variables in an 'if' statement in Bash? How can I visualize the file system usage on Windows? How can I visualize which folders and files are taking up all of the space on my hard drive?  I'm getting some conflicting reports on the size of hard drive contents. Namely what is and isn't there and what folders are actually using the space.   I need to know which of the files or folders the culprits behind all this hidden bloat. Also there should be a print option to get it on paper. How to list all functions in a Python module? Book for proof writing How does accepting an answer work? What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the . I have just booted my clean Ubuntu 18.04 LTS VM and tried to install some application with sudo apt install.  But got error message:     E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)       E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), is another process using it?   What process created the /var/lib/dpkg/lock-frontend file in Ubuntu? How to gently stop it and take manual control on APT? Exporting Data From Salesforce - REST or SOAP? We have a requirement where we need to export records from salesforce tables into our application programmatically. I am reading on the various API's for data integration from salesforce mainly SOAP vs REST API's.  From what I understand, REST should be used when the web service requests are from mobile devices or browser based clients (since they understand JSON). Is that true? If that's the case how do Bulk REST API's fit the bill (since they are meant for bulk data transfers)?  I would like to get your thoughts on what are pros and cons in using SOAP or REST API's to export data records. Note that the requests are being made a java ee server application programmatically. After retrieving the records (probably in batches) from salesforce records we process (validate, filter etc) them and load them in our internal tables.  Thanks. How should I budget for ally/third party NPCs in 4e combats? I've done a few combats recently where the PCs and their enemies were not the only participants in the fight.  I wasn't sure how to budget XP in this case.  In the case of an NPC ally to the PCs, I see two options.     Draw the NPC up as a PC and increase the number of members in the party.    Draw the NPC up as an NPC and take its XP into account when budgeting.   I'm not sure if either option is correct, or if there are others.  But the ambiguity doesn't end there - what about if there's more than one side in the fight and nobody wants to team up?  I'd rather not treat it as one combat budget divided over two factions.  Unless the factions immediately unite, it's going to be an absurdly easy combat.  Would I be better off budgeting for two encounters than happen at the same time, and hoping that no PC gets ganged up on too much?  In general, how is XP budgeting done in complex combats with NPC allies and/or more than two factions? My brother owns Skyrim on steam. We use Steam Family Share, but we were wondering how both of us could play it at the same time? How to prove that a compact set in a Hausdorff topological space is closed? AuraClientService.postProcess: error in processing [RangeError: Maximum call stack size exceeded] - Client Side Action I have a lightning component that is using ui:inputSelect.   The component code:              &lt;div class="slds-form-element__control"&gt;                 &lt;ui:inputSelect class="slds-select" aura:id="quals" change="{!c.getPreCodes}"&gt;                     &lt;aura:iteration items="{!v.questions}" var="q"&gt;                          &lt;ui:inputSelectOption aura:id="question" text="{!q.Id}" label="{!q.Question_Text__c}"/&gt;                     &lt;/aura:iteration&gt;                 &lt;/ui:inputSelect&gt;             &lt;/div&gt;   The controller:      getPreCodes : function(cmp, event, helper){         var selected = cmp.find("quals").get("v.value");          var action = cmp.get("c.getPreCodes");         action.setParams({             "qualID" : selected         });         action.setCallback(this, function(response){             var state = response.getState();             if (state === "SUCCESS") {                  console.log('precodes: ', response.getReturnValue());              }         });          $A.enqueueAction(action);     }   The basic logic is that the uiSelect is dynamically populated on init (this works fine). When a user makes a selection the "change" parameter function is fired to retrieve a list from the database and pass it to another component.   However, the change function {!c.getPreCodes} seems to be called recursively causing a      "Something has gone wrong. AuraClientService.postProcess: error in   processing [RangeError: Maximum call stack size exceeded] . Please try   again."   error. If I comment out the enqueueAction the function only runs once (nothing is called recursively) so I suspect it has something to do with the controller call. Digonalizable Polynomial Matrix For any polynomial $p(x) = a_0 + a_1x + · · · + a^kx^k$ and any square matrix A, $p(A)$ is defined as $p(A) = a_0I + a_1A + · · · + a_kA^k$. Show that if v is any eigenvector of A and $χ_A(x)$ is the characteristic polynomial of A, then $χ_A(A)v = 0$, Deduce that if A is diagonalizable then $χ_A(A)$ is the zero matrix.  I got that $p(\lambda)$ is the eigenvalue of $p(A)$ and if A is diagonalizable then $χ_A(x)$ is the zero matrix since p(A) is similar to its diagonal matrix p(D)  $$p(D) = a_nD_n + · · · + a_1D + a_0I$$  =  $\begin{matrix} p(\lambda_1) &amp;0&amp;...&amp;0\\0&amp; p(\lambda_2)&amp;...&amp; 0 \\ ...&amp;...&amp;...&amp;...\\0&amp;0&amp;... &amp; p(\lambda_n) \end{matrix}$ What is the difference between independent and mutually exclusive events? "The ticket is printing" vs "...is being printed" You're standing in front of a ticket vending machine and it says "The ticket is printing". Is that correct or should it be "The ticket is being printed"?  EDIT:  If both are correct, which one should be preferred or is more common? What's the "official" explanation for Harry's (and everyone else's) absence from muggle school? So a bunch of kids all of a sudden "go missing" from school.  Harry Potter having attended school for a couple of years before starting at Hogwarts, one semester just doesn't show up.  How is this solved? What do parents say when a school teacher calls and wonders where their pupil is?  I assume that Hogwarts isn't an officially recognized school (though perhaps it is?), and due to education being compulsory, someone would do the math and find that low-hundreds of kids go missing in the transition from primary to secondary school every year.