Is the question in the Munkres's topology book wrong?
The set of homotopy classes
Which is correct: "what if there was" or "what if there were"? Possible Duplicate:          Is this correct grammar?     What if there was a Stack Overflow on…    Shouldn't it be "what if there were a Stack Overflow on…"? No internet connection after ubuntu server 20.04 install, ifconfig not available I recently installed Ubuntu Server 20.04 LTS on my desktop, and found out there was no internet connection even though I had the LAN cable connected. ifconfig and iwconfig failed saying the corresponding packages net-tools and wireless-tools were not installed.   EDIT  Here is the info requested. Please find the image How exactly does a  work?  This is an extremely broad question. What code keeps things bouncing against each other, what code makes the player walk into a wall instead of walk through the wall? How does the code constantly refresh the players position and objects position to keep gravity and collision working as it should?  If you don't know what a collision engine is, basically it's generally used in  to make the player acutally hit walls and the like. There's the 2D type and the 3D type, but they all accomplish the same thing: collision.  So, what keeps a collision engine ticking? Etiquette for revision comments Using Unicode Zero Width Spaces allows all space comments This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it? Can you stay in Turkey for over 90 days within the 180 day visa period but split over different visits? The Turkish e-visa is valid for a period of 180 days and allows you to stay for a maximum of 90 days. Am I allowed to stay for say 50 days, then another 50 days, over two different visits within the 180 day period?  I'm looking at the e-visa website  and it doesn't seem to be too clear on this. Diagonal straight lines in residuals vs fitted values plot for multiple regression I am observing strange patterns in residuals for my data:   [EDIT] Here are the partial regression plots for the two variables:      [EDIT2] Added the PP Plot   The distribution  seems to be doing fine (see below) but I have no clue where this straight line might be coming from. Any ideas?   [UPDATE 31.07]  It turns out you were absolutely right, I had cases where the retweet count was indeed 0 and these ~ 15 cases resulted in those strange residual patterns.   The residuals look much better now:   I've also included the partial regressions with a loess line. How do I erase/format a harddisk from a live CD? I need to format a drive containing an old install of Ubuntu 10.04, to install Vista (not my idea!) Vista setup apparently refuses to format non-FAT32 or NTFS partitions. However, I can't seem to format it from my live CD (Ubuntu 11.04) at all; I keep getting "device is busy" errors. What is the simplest way to format this drive? Proving the sum of two independent Cauchy Random Variables is Cauchy Is there any method to show that the sum of two independent Cauchy random variables is Cauchy? I know that it can be derived using Characteristic Functions, but the point is, I have not yet learnt Characteristic Functions. I do not know anything about Complex Analysis, Residue Theorem, etc.   I would want to prove the statement only using Real Calculus. Feel free to use Double Integrals if you please.   On searching, I found . However, I was wondering if I could get some help directly on the convolution formula:  $$f_Z(z)=\int_{-\infty}^\infty f_X(x)f_Y(z-x)\,dx=\int_{-\infty}^\infty\frac{1}{\pi^2}.\frac{1}{1+x^2}.\frac{1}{1+(z-x)^2}dx\tag{1}$$  Here I have supposed that $X,Y$ are Independent Standard Cauchy. But I think the general formula can be derived easily after some substitutions. I need some help on how to proceed from $(1)$.  EDIT: Just as what the hint in the hyperlink said, I got the answer using that hint. However, I am not quite sure that the hint is algebraically correct. Maybe there has been some typing mistake in the book. Hyperlinks to web sites using anchors sometimes don't work I am using gedit text editor with embedded terminal in ubuntu 12.04. I'm trying to search for some text using grep. I want to search for this line of code   'type' =&gt; 'select'   I tried:  grep -r '\'type\' =&gt; \'select\''  But grep didn't return any results.  So can someone kindly tell me how to search for the code above? The  contains a link to the new code of conduct,  . As of 2018-08-07T05:27:38+00, . Also, I cannot find any other link to the conduct yet, neither in the help center, nor in the site navigation, which is a bummer, given that we're invited to read the new CoC:     Really, please, take a moment to read the new Code of Conduct now. It’s not long, it’s not wordy-and-legalese-y and in our long held tradition, we feel that it does a good job of assuming that the vast majority of folks that use our sites always have the best intentions at heart.    Is the code of conduct not yet published?  Edit: As mentioned in the comments,  announces the conduct and links to , so maybe it's not public yet? Carrying a handgun in other countries with a US concealed carry permit Is there a limit to the number of magic rings a character can wear on one hand? How do you fix a bad merge, and replay your good commits onto a fixed merge? Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic. I was thinking that the product of groups $\mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}/2\mathbb{Z}$ is not cyclic, but $\mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}/p\mathbb{Z}$ is cyclic if p is an odd prime. Then I found logic that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is certainly cyclic if $m$ and $n$ are coprimes.  I searched on google a proof of that, to compare with mine and the answer is that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is isomorphic to $\mathbb{Z}/mn\mathbb{Z}$ (which is clearly cyclic) $\iff$ $m$ and $n$ are coprimes.  But I got another proof and I want to know what you think about it :     I claim that $([1]_m,[1]_n)$ generates $\mathbb{Z}/m\mathbb{Z}$   $\times\mathbb{Z}/n\mathbb{Z}$, where $[a]_d$ is the canonical   projection of $a\in \mathbb{Z}$ into $\mathbb{Z}/d\mathbb{Z}$.       Let's take multiples of $([1]_m,[1]_n)$ until we get $m \cdot$   $([1]_m,[1]_n) = ([0]_m,[m]_n)$ (where I suppose $m=\min(m,n)$...   otherwise, consider $\mathbb{Z}/n\mathbb{Z}$   $\times\mathbb{Z}/m\mathbb{Z}$ and $\min(m,n)=n$).       The next step is $([1]_m,[m+1]_n)$. This pair is not equal to   $([1]_m,[1]_n)$, since $m+1 \not\equiv1$ mod $n$ ($m$ and $n$ are   supposed to be coprimes). We can now continue adding $([1]_m,[1]_n)$   to the results.      The last step is precisely reached when you got   $([mn]_m,[mn]_n)=([0]_m,[0]_n)$. At this point, the fact that $m$ and $n$ are coprimes is absolutely necessary because if they are not coprimes, $lcm(m,n)\ne m\cdot n$ and   $([lcm(m,n)]_m,[lcm(m,n)]_n)=([0]_m,[0]_n)$ but all the $m \cdot n$ possible pairs are not reached, only the $lcm(m,n)$ are ! Proof of Steinitz Theorem I want a source containing the proof of Steinitz Isomorphism Theorem stating:     For any Dedekind domain $R$ and any two nonzero ideals $I$ and $J$ of $R$ we have $I⊕J≅R⊕IJ$.   Thanks! Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$ Cleaning my Macbook Pro Retina leaves greasy 'streaks' across the screen