Direct sum of groups vs product
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
Importing two classes with same name. How to handle? Identify a movie in which aliens believed a sci-fi TV show to be true documentary I remember watching a sci-fi movie in the early 00s. It was full of comedy. Here are the details I recalled:   There was a space opera TV show in the movie. It seemed a true copy of Star Trek (they used to pilot a ship and there were captain, first officer, science officer etc on bridge). The name of the TV show was possibly the name of the movie. Once the main crew of the TV show were celebrating some achievement, they were approached by humans having weird behavior (they were actually aliens in disguise; in reality, they looked like octopus). The alien race was innocent. They couldn't comprehend the concept of art, lies etc. So, they believed that the TV show (they got the EM waves) was true historical documentary of mankind. So, they came looking for help from the brave captain of the show. From the TV show details, they had built a starship which really worked. The aliens needed the TV show crew to pilot the ship to defeat another alien race which terrorized them. The TV show crew didn't have any problems piloting the ship as the controls were familiar, only these controls were real.   Can you please identify the movie? I am an international student in the US (important as my stay in US is tied to my student visa, issued to attend my current university).  I joined as a grad student in the MS CS program in one of the okayish public universities (ranked ~50 on QS/US news). I joined in Fall '18 and am still in my first semester. I took all the so-called "difficult" courses, but I find them very trivial (considering my undergrad was from a very good university). I am very disappointed with the curriculum and feel the coursework is not at all rigorous for a grad-school.  I might sound super arrogant, but I feel out-of-place when I talk to other students and hear them cringe about how hard the courses are, or how they don't have enough time to finish assignments within the deadlines as I find all of the coursework very trivial and feel that the assignments are a joke.   Fortunately, I am working with one of the best profs the university has to offer on a very impactful project and the research is going great. But that's the only plus point I see from sticking around.  My aim from grad school is to get research experience and join one of the Big 4s or upcoming CS unicorn startups. I cannot see myself joining one of the Big-Ns after graduating since the students from this school rarely bag a Google/Fb/unicorn startup job.  Since December is the Fall'19 admissions deadline, I am thinking about reapplying to those top 10 CS schools which I couldn't get into last year (probably because of my poor undergrad GPA).   On the other hand, since every CS company just asks leetcode-style questions in interviews, I can just be super good at it and try to nail whatever interview I get without wasting another year and then doing the same.  I'm not really interested in any kind of credit transfer either since I would like to start fresh in a more rigorous curriculum.  I'm not sure if switching schools would be a wise decision and could really use some advice from the community here.  PS :  Probably related -   Posting with a dummy account for anonymity. Are split infinitives grammatically incorrect, or are they valid constructs? Mark's generosity in this crisis seems to more than make up for his earlier stinginess.   Should those sentences always be avoided, or are there cases where they are valid? Why does the 'b' in absorb change to a 'p' in absorption? Proof that Limit of the Log is the Log of the Limit Proof that Limit of the Log is the Log of the Limit. What is the intuition behind this statement? 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) Are the WotC archives of d20 Character Optimization forum forever lost? I was looking for the Wizard Handbook but all the links were broken.  Somewhere on the handbooks of other classes (on other forums) I saw a      This was archived by WotC, here's the link   But the link leads to the welcome page of WotC (since it's broken).  Is there a way to get all that info back? Do you know where to get it from? The Wayback Machine did not archive the forums. Is an Otyugh's grapple different from a standard grapple? In 5e to escape a Grapple check, I know you roll athletics (str) or acrobatics (dex) opposed by an athletics (str) check.  In the Otyugh entry in the Monster Manual it doesn't say there's any check, instead it assigns a set DC for an "escape" (DC 13... which is a str check with a 10 assigned as the "roll").    So the question is:    Does the Otyugh actually make a roll in this instance (like the general rule) or does it have a set DC (for the specific case) OR is it just a poorly communicated version of the GENERAL rule being played out?   A little clarification on this would be AWESOME. In the event of a "specific vs general" scenario, what actually is the "escape" roll?  What modifier is applied? None? Prove: The pre-image of an ideal is an ideal. Let $\phi : R \to S$ be a homomorphism. If $N$ is an ideal of $S$, then $\phi ^{-1} (N)$ is an ideal of $R$. How are House points tabulated/tracked? I was writing some Unit tests last week for a piece of code that generated some SQL statements.  I was trying to figure out a regex to match SELECT, INSERT and UPDATE syntax so I could verify that my methods were generating valid SQL, and after 3-4 hours of searching and messing around with various regex editors I gave up.  I managed to get partial matches but because a section in quotes can contain any characters it quickly expands to match the whole statement.  Any help would be appreciated, I'm not very good with regular expressions but I'd like to learn more about them.  By the way it's C# RegEx that I'm after.  Clarification  I don't want to need access to a database as this is part of a Unit test and I don't wan't to have to maintain a database to test my code. which may live longer than the project. How can I SELECT rows with MAX(Column value), PARTITION by another column in MYSQL? Site choice dropdown cannot be shown on Android app Steps to reproduce:   Ask a question, open the "Ask on which site?" dropdown menu. Press the back button.   Issue: the menu will disappear and you can't bring it back by tapping the arrow or the field. Only typing text or selecting another field then tapping back will return the dropdown menu. When I run the following query in query editor I get this error.  Error     Unknown error parsing query   Query  SELECT Id, OwnerId,Account.OwnerId FROM Contact where OwnerId = Account.OwnerId limit 100   Does anybody know what the problem is? Resolve $\lim_{x \to 0} \frac {\tan 3x}{\tan 5x}$ I started resolving this limit:  $$\lim_{x \to 0} \dfrac{\tan 3x}{\tan 5x}$$  so:  $$\begin{align}\lim_{x \to 0} \dfrac{\tan 3x}{ \tan 5x} &amp; = \lim_{x \to 0} \dfrac{\frac{\sin 3x}{\cos 3x }}{\frac{\sin 5x}{\cos 5x}} \\ \\ &amp; = \lim_{x \to 0} \dfrac{ \sin (3x) \cdot \cos (5x)}{ \sin(5x) \cdot \cos (3x)}\\ \\ &amp; = \quad?\end{align}$$  Could someone help me please Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$ Let $A$ be the following subset of $\mathbb{R}^{2}$:$$A=\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x&gt;0\}$$ Then  $1.$ $A$ is connected.  $2.$ $A$ is compact.  $3.$ $A$ is path connected.  $4.$ $A$ is bounded.  It is clear that $A$ is unbounded as the graph of $x\sin(\frac{1}{x})$, so option $2$nd and $4$th are not correct. Again $A$ is connected by using the fact that closure of connected set is connected. But i am confused about path connectedness of $A$. Please help me about path connectedness of $A.$ Thanking you. Why is it important to override GetHashCode when Equals method is overridden? What element saved Iron Man from his blood poisoning? I just watched Iron Man 1&amp;2 the other day. I'm new to the entire story. In IM2 we learn that his blood is being poisoned and that he has tried every combination of every existing element as a cure - unsuccessfully. Then he deducts &quot;the key&quot; from the Expo park's plans which saves him. What is that key? What element had he not tried? I realize that the movie story has to be simplified, compared to the original story, so there are probably story elements that I have completely missed because they're only in the original works. We also saw that in LOTR. How can I upgrade from Mac OS X Tiger 10.4? If I buy a regular retail Snow Leopard disc (i.e. the £25 version), can I use it to upgrade a Mac from Tiger (10.4)?   on the Apple Store’s Q&amp;A site suggests it’ll work, but Apple seem to imply that you need the (significantly more expensive) Mac Box Set (“”).