The torus is connected
Connected compact covering space of torus is homeomorphic to $S^1\times S^1$
I see in my company's IT installations that there are numerous disks with one partition occupying all of the space on disk. There is typically something like a /dev/sdb with a partition /dev/sdb1, and the size of /dev/sdb1 is the size of the whole block device. The partition is then mounted with the required file-system format, mountpoint etc.  I do not understand why we would use a partition rather than the whole disk for such (1-partition) configurations. Is there any reason why a partition would be used in this case rather than a whole disk ? Are there any best practices that recommend this approach ?  For example, we could create a Filesystem on a whole raw block device and mount it without needing any partition:  mkfs.ext4 -E stride=16,stripe-width=64 /dev/xvde mount /dev/xvde /mnt/abc   That creates a mountpoint without a specified partition. As a verification:  # sfdisk -l /dev/xvde  Disk /dev/xvde: 6527 cylinders, 255 heads, 63 sectors/track  # fdisk -l /dev/xvde  Disk /dev/xvde: 53.7 GB, 53687091200 bytes, 104857600 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes   For something with a partition, we get the list of partitions under it:  # fdisk -l /dev/sdb  Disk /dev/sdb: 2000.4 GB, 2000398934016 bytes, 3907029168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk label type: dos Disk identifier: 0x00082e8c     Device Boot      Start         End      Blocks   Id  System /dev/sdb1            2048  3907026943  1953512448   83  Linux   My fundamental question is this: Is there some advantage in creating a partition and then creating a filesystem on that partition, as compared to creating a filesystem on the whole disk and then mounting the whole disk ? Change the URL in the browser without loading the new page using JavaScript How would I have a  action that may have some effects on the current page but would also change the URL in the browser so if the user hits reload or bookmark, then the new URL is used?    It would also be nice if the back button would reload the original URL.  I am trying to record JavaScript state in the URL. How to concatenate a variable number of csv, removing their header rows? I've played around in the past of the 2D Flash fan-made version of the popular Valve game Portal.  It has basically the exact same mechanics, but as a 2D side-view flash game.  Lately I've toyed around with creating a simplified flash version of some of my favorite franchises (such as Zelda, Mario, Splinter Cell, etc.).  Of course, nothing is "stopping" me from just using the same mechanics and just changing the name to something not copyrighted.  I have witnessed projects that have tried to directly port a 3D game into a 2D simplified version, with the exact same plot and puzzles (Ocarina of Time in 2D comes to mind), and I have seen them being shut down.  But I am not likely going to exactly duplicate any game...just borrow some of the source material and basic underlying mechanics.  For example, if I were to make a Zelda-influenced fan game, I would have items such as the Hookshot, Boomerang, and all other sorts of ones from the Gameboy Zeldas; just with a custom plot and dungeons.  With likely the same mechanics.  What are the legal issues involved in this?  I used to think it was a "Don't do this ever; it's a bad idea."  But then I've seen the Portal clone, and now I'm curious. $\lim_{x \rightarrow \infty} \lim_{n \rightarrow \infty} f_{n}(x) = \lim_{n \rightarrow \infty}\lim_{x \rightarrow \infty}f_{n}(x) $ in case of uniform convergence of $f_{n}(x)$ to $f(x)$  I used this while I was given that $f_{n}(x)$ converges to $f(x)$ uniformly. Is this correct and I was also thinking to prove this! Mirror cells so that a change in either cell updates the other I have 2 cells containing the same picklist values on separate sheets. I want the cells to mirror each other so that whenever I choose a new value in either sheet 1 or sheet 2, the value on the other sheet is updated to match the newly selected value. Is this possible?  UPDATE   Worksheet 1:   Worksheet Name: 'Live Forecast Tool' Cell containing picklist: C3:D3 (merged) Picklist values within range: ='SF MRF'!H5:Y5  Worksheet 2:   Worksheet Name: 'AH' Cell containing picklist: C3:D3 (merged) Picklist values within range: ='SF MRF'!H5:Y5    Cell C3:D3 needs to update to show the value that has been changed on the other sheet. Let S be a finite set.Let F be a surjective function from S to S.  How do I prove that it is injective? Why isn't it $E \approx 27.642 \times mc^2$? Why is it that many of the most important physical equations don't have ugly numbers (i.e., "arbitrary" irrational factors) to line up both sides?   Why can so many equations be expressed so neatly with small natural numbers while recycling a relatively small set of physical and mathematical constants?  For example, why is mass–energy equivalence describable by the equation $E = mc^2$ and not something like $E \approx 27.642 \times mc^2$?  Why is time dilation describable by something as neat as $t' = \sqrt{\frac{t}{1 - \frac{v^2}{c^2}}}$ and not something ugly like $t' \approx 672.097 \times 10^{-4} \times \sqrt{\frac{t}{1 - \frac{v^2}{c^2}}}$.  ... and so forth.    I'm not well educated on matters of physics and so I feel a bit sheepish asking this.   Likewise I'm not sure if this is a more philosophical question or one that permits a concrete answer ... or perhaps even the premise of the question itself is flawed ... so I would gratefully consider anything that sheds light on the nature of the question itself as an answer.    EDIT: I just wished to give a little more context as to where I was coming from with this question based on some of the responses:  @Jerry Schirmer comments:      You do have an ugly factor of $2.997458 \times 10^8 m/s$ in front of everything. You just hide the ugliness by calling this number c.   These are not the types of "ugly constants" I'm talking about in that this number is the speed of light. It is not just some constant needed to balance two side of an equation.  @Carl Witthoft answers:      It's all in how you define the units ...   Of course this is true, we could in theory hide all sorts of ugly constants by using different units on the right and the left. But as in the case of $E=mc^2$, I am talking about equations where the units on the left are consistent with the units on the right, irrespective of the units used. As I mentioned on a comment there:     $E=mc^2$  could be defined using units like $m$ in imperial stones ($\textsf{S}$), $c$ in cubits/fortnight ($\textsf{CF}^{−1}$) and $E$ in ... umm ... $\textsf{SC}^2\textsf{F}^{−2}$ ... so long as the units are in the same system, we still don't need a fudge factor.   When the units are consistent in this manner, there's no room for hiding fudge constants. Proof that every repeating decimal is rational Out-of-control starship results in some crew members landing in a rebirthed universe? For only my index pages, I am receiving this warning in Google Search Console:     Duplicate, submitted URL not selected as canonical   I know that this occurs because Google is attempting to track both the default landing "page" (i.e. www.domain.example/) and the page to which to which DirectoryIndex points (i.e. www.domain.example/index.html). They are, in fact, the same page, and so the warning is the result of a false positive.  Two questions for our community:   Why does Google not conflate these and count them as a single page? Alternately, is there something wrong with my set up if this has happened? I can easily force both pages to point to a single canonical URL. But which is preferable, "/" or "index.html"? I am just a high school student, and I haven't seen much in mathematics (calculus and abstract algebra).  Mathematics is a system of axioms which you choose yourself for a set of undefined entities, such that those entities satisfy certain basic rules you laid down in the first place on your own.  Now using these laid-down rules and a set of other rules for a subject called logic which was established similarly, you define certain quantities and name them using the undefined entities and then go on to prove certain statements called theorems.  Now what is a proof exactly? Suppose in an exam, I am asked to prove Pythagoras' theorem. Then I prove it using only one certain system of axioms and logic. It isn't proved in all the axiom-systems in which it could possibly hold true, and what stops me from making another set of axioms that have Pythagoras' theorem as an axiom, and then just state in my system/exam "this is an axiom, hence can't be proven".  EDIT : How is the term "wrong" defined in mathematics then ? You can say that proving fermat's last theorem using the number-theory axioms was a difficult task but then it can be taken as an axiom in another set of axioms .  Is mathematics as rigorous and as thought-through as it is believed and expected to be ? It seems to me that there many loopholes in problems as well as the subject in-itself, but there is a false backbone of rigour that seems true until you start questioning the very fundamentals . When to use the double not (!!) operator in JavaScript Python and regular expression with Unicode I need to delete some Unicode symbols from the string 'بِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِ'  I know they exist here for sure. I tried:  re.sub('([\u064B-\u0652\u06D4\u0670\u0674\u06D5-\u06ED]+)', '', 'بِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِ')   but it doesn't work. String stays the same. What am I doing wrong? What is the Necessity of $...$ Around Numbers? I typed up an assignment with a lot of numbers in LaTeX and turned it in to my adviser.  When he returned it to me with some corrections, one of which was a lot of $ around my numbers.  I understand that $ are necessary around some mathematical formulas, but I was just using numbers like -2 and 4.  I did not see any change in the font of the numbers when I added the $ either.  Since my adviser did not want to give me an explanation, what is the rationale? How can I move Steam games to another disk? Weighing a flying bird traceroute TCP equivalent for Windows Too many requests? I went to stackexchange.com and clicked on SO.  After a few minutes I got a message saying "We have detected too many requests from this IP.  If this is an error contact us."  That was the second SE page I tried to visit.  Second only to SE.com  I moved to another machine and it's working now.  The first machine usually works, I don't know if a got assigned a blacklisted IP or what.  Anyone know what's going on?  EDIT: I would really rather not post my IP on the web, but if a diamond or dev asks I'll email it.  EDIT 2: I looked at badp's dupe suggestion and can verify that I have no scripts frequently calling SO. Hartshorne Theorem 8.17