I am sorry if this has been asked before.  I read the following in a textbook:     The examples are intentionally simple, so we can focus on the language features.   I thought that     The examples are intentionally simple so that we can focus on the language features.   is correct.  Can someone clarify?
A book suggests that we should not interchange "so" and "so that". "So" means "therefore", and "so that" means "in order that". However, it seems to me that in many cases they don't actually have a difference. For example:     Alice got up at 5:00 A.M., so that she could drive her son to school.   If I substitute "so that" with "so", this sentence presents the exact same causal relation to me:     Alice got up at 5:00 A.M., so she could drive her son to school.   I must have missed something here, since English is my second language. Could somebody explain the difference?
If I have an i.i.d. random variables $X_i$ from a uniform distribution on $[0,1]$.   How would I find scaling sequences $a_n$, $b_n$ such that $a_n(M_n − b_n)$ converges in distribution to a non-trivial limit function $G$ for  $ Y_i = X_i,$ and $M_n = \max(Y_1,...,Y_n) $ Bring all planes in mesh to same level I have added a plane in top view. I have then extruded the plane according to a floorplan in topview.  I don't know what happened, but when I switched my view, I could see that some parts of it are for some reason high up in the air.  I would like to ask how I can bring everything back down onto the grid / floor.  And if somebody could tell me how this might have happened, I would also be glad. I'm a quarter Draconian, a quarter Dragonborn and half Half-Dragon? What are the differences between "Dragonborn", "Half-Dragon", and "Draconian" races in D&amp;D?  In the Hoard of the Dragon Queen adventure, for example there is  a Half-Dragon npc. I had assumed that when writing the adventure they were only allowed to use known material from Basic, and so renamed the Dragonborn into "Half-Dragon" for the sake of compatibility etc. However, the dragon breath rules are not at all similar for the half-dragon and the dragonborn, and I've also noticed wiki article that imply that they are different races entirely. (Thus introducing me to the term Draconian)  Are there clear differences between these three races, (in the same way there are differences between Goblins and Hobgoblins, or Dragonborn and Lizardfolk and Kobolds,) or are they really just three different setting names for the same basic race?  Answers can either be D&amp;D 5e specific, or be based on the lore from all editions of Dungeons and Dragons. (I'm assuming here that the answer will be the same regardless)  Here are two images, the first one is a "half-dragon" from the front of the Hoard of the Dragon queen module, and the second one is a "dragonborn" from the 5e player's Handbook.  I've included these images to help explain my confusion. My C# application is returning 0xE0434352 to Windows Task Scheduler but it is not crashing Nsolve gives solutions with a small complex part which can't be eliminated by chop command Getting different answers when integrating using different techniques Question:  Is it possible to get multiple correct results when evaluating an indefinite integral?  If I use two different techniques to evaluate an integral, and I get two different answers, have I necessarily done something wrong?    Often, an indefinite integral can be evaluated using different techniques.  For example, an integrand might be simplified via partial fractions or other algebraic techniques before integration, or it might be amenable to a clever substitution.  These techniques give different results.  For example, looking over a few other questions on MSE:      From : evaluate $$ \int x(x^2+2)^4\,\mathrm{d}x. $$    Via the substitution $u = x^2+2$, this becomes $$ \int x(x^2+2)^4\,\mathrm{d}x       = \frac{1}{10}x^{10} + x^8 + 4x^6 + 8x^4 + 8x^2 + \frac{32}{5} + C.     $$ However, multiplying out the polynomial and integrating using the power rule gives $$ \int x(x^2+2)^4\,\mathrm{d}x       = \frac{1}{10}x^{10} + x^8 + 4x^6 + 8x^4 + 8x^2 + C    $$     From :  evaluate   $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x. $$    Simplifying the integrand using partial fractions then integrating gives $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x       = \frac{-2}{(x+1)} - \ln|x+1| + C.    $$ Via integration by parts, we get $$ \int \frac{1-x}{(x+1)^2} \,\mathrm{d}x       = \frac{x-1}{(x+1)} - \ln|x+1| + C.    $$     From : evaluate   $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x. $$    Using the substitution $u = \sec(\pi x)$, this becomes $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x       = \frac {\sec^2(\pi x)}{4\pi} + C.    $$ Using the substitution $u = \tan(\pi x)$, this becomes $$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2\,\mathrm{d}x       = \frac {\tan^2(\pi x)}{4\pi} + C.    $$ Why does the reputation need to be publicly displayed? Possible Duplicate:          The idea of getting greater privileges with greater reputation is good, but what is the benefit of publicly displaying that reputation? Since SO claims to be about good questions and answers, that purpose is better served if the reputation is only visible to the account owner (and, of course, the site admins). This would better ensure that content gets pushed up solely by its merit, and not based on the author. (See )   Edit (copied from comment to an answer below): Once you have gathered high reputation, you can also gather more reputation with ordinary answers, especially from newbies (newbies on the topic, not on the site) who usually choose to accept or upvote an answer on the assumption that "since a high-rep user has posted it, it is probably right". Can you guarantee that doesn't happen often? Are $\mathbb{Z_p},\mathbb{Q},\mathbb{R},\mathbb{C}$ above themselves vector space? Is a field above anoother field a vector space?   As for 1. we know that $\Bbb R^n$ is a vector space so in particular it is true for $n=1$  For 2. by definition a vector space is $V$ with addition and multiplication over a field, therefore 2 is true. Can there be multiple paths for which Fermat's least time principle can be obeyed? Can there be more than one path for which Fermat's least time principle is obeyed? What are the main differences between VirtualBox networking types? I'm trying to use VirtualBox to host a couple of VMs.  Each VM should be able to connect to the Internet (this is needed primarily to install software) My Host browser should be able to connect to the Guest VMs.  Also I need to be able to ssh to the Guest VMs.     This is why I want each VM to have a static IP address.     This will also allow the VMs to connect to each other, say for database connectivity.  I have done this with VMware Fusion.  However, VMware has lately bitten me too often and destroyed so much work that I want to try VirtualBox.  But I'm not a network guru and don't know which type of networking I want.  So what I'm asking is simple:  What are the main differences between networking types. This could help me find out which type of networking I should use in my case.  And of course if anyone has a link to any documentation of how to do what I want, that would be greatly appreciated.  Thanks, ge In comments, moderators have their diamonds in the OP rectangle:        And in the review (suggested edits), mods have their diamonds outside the blue OP background highlight rectangle:        Of course, it Doesn't Really Matter At All, but it is a small discrepancy (I am not saying that in the review, OP rectangles have a bigger padding). UK Visa Refused - can I reapply immediately? Do Chinese citizens require a visa to go to Hong Kong for less than 7 days? As I show below, typical alien depictions include an elongated, pale face, two dark elliptical eyes, and a small mouth.  Who first used this design for an alien?  Where does this design come from? Im having trouble with the second part of this question,  Let $H$ be a normal subgroup of $G$ with $|G:H| = n$,  i) Prove $g^n \in H$ $\forall g \in G$ (which i have done)  ii) Give an example to show that this all false when $H$ is not normal in $G$.(which I am having trouble with showing)  Any suggestions? Which form should be used for at­tribu­tive nouns like “stu­dent union”: sin­gu­lar or plu­ral, or pos­ses­sive sin­gu­lar or pos­ses­sive plu­ral? When should a noun that’s used at­tribu­tively to de­scribe an­other  noun be plu­ral, and when should it be sin­gu­lar?  And when should it be pos­ses­sive, like bak­er’s dozen and when should it be plu­ral pos­ses­sive, like farm­ers’ mar­ket?  In other words, why do we say teach­ers union rather than teacher  union?  And why do we say wed­ding plan­ner rather than wed­dings plan­ner?  Which of these vari­ants is or are cor­rect?        stu­dent union   stu­dents union   stu­den­t’s union   stu­dents’ union      What about com­mu­nity val­ues ver­sus com­mu­ni­ty’s val­ues?  Please note I am look­ing for a gen­eral rule or at least some tips.  These are only ex­am­ples.  Up­date: It seems even na­tive speak­ers fol­low their per­sonal  style to write such com­pound words. I won­der why in the IELTS lis­ten­ing sec­tion, the lan­guage learner has to write a spe­ci­fic form and there is no rule for this. ETS() function, how to avoid forecast not in line with historical data? I am working on an alogorithm in R to automatize a monthly forecast calculation. I am using, among others, the ets() function from the forecast package to calculate forecast. It is working very well.  Unfortunately, for some specific time series, the result I get is weird.  Please, find below the code i am using :  train_ts&lt;- ts(values, frequency=12) fit2&lt;-ets(train_ts, model="ZZZ", damped=TRUE, alpha=NULL, beta=NULL, gamma=NULL,              phi=NULL, additive.only=FALSE, lambda=TRUE,              lower=c(0.0001,0.0001,0.0001,0.8),upper=c(0.9999,0.9999,0.9999,0.98),              opt.crit=c("lik","amse","mse","sigma","mae"), nmse=3,              bounds=c("both","usual","admissible"), ic=c("aicc","aic","bic"),             restrict=TRUE)   ets &lt;- forecast(fit2,h=forecasthorizon,method ='ets')      Please, you will find below the concerned history data set :   values &lt;- c(27, 27, 7, 24, 39, 40, 24, 45, 36, 37, 31, 47, 16, 24, 6, 21,  35, 36, 21, 40, 32, 33, 27, 42, 14, 21, 5, 19, 31, 32, 19, 36,  29, 29, 24, 42, 15, 24, 21)   Here, on the graph, you will see the historical data (black), the fitted value (green) and the forecast(blue). The forecast is definitely not in lines with the fitted value.  Do you have any idea on how to "bound" the forecat to be "in line" with the historical sales? I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) Why does an unhinged body rotate about its centre of mass? virtual methods