I got a problem upgrading packages on Ubuntu 12.04.5 LTS
Not enough space in /var/cache/apt/archives/
Does the speed of light vary in non-inertial frames? Proof of uniform limit of Continuous Functions The uniform limit of Continuous Functions is continuous.   Proof Let $\varepsilon &gt; 0$. There exists $N$ in natural numbers such that $n&gt;N$ implies  $|f_n(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. In particular $|f_{N+1}(x)-f(x)| &lt; \frac{\varepsilon}{3}$ for all $x$ in $S$. Since $f_{N+1}$ is continuous at $x_0$ there is a $\delta&gt;0$ such that, $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f_{N+1}(x)-f_{N+1}(x_0)|&lt; \frac{\varepsilon}{3}$ Now we conclude $x$ in $S$ and $|x-x_0| &lt; \delta$ imply $|f(x)-f(x_0)|&lt; 3 \cdot \frac{\varepsilon}{3} = \varepsilon$.  Can someone explain what is happening here? I don't follow it all. Show that a Cauchy sequence has a fast-Cauchy subsequence "Comments only" lock notice on closed questions mistakenly says that question is still accepting answers When a question has a &quot;comments-only&quot; lock, the following notice is displayed on top of the question:  Locked for X days. Comments on this question have been disabled, but it is still accepting new answers and other interactions.  However, I noticed that if the question is closed (even before the lock), the same notice is used:  ..which could be confusing, especially for new users. Proposed change to the notice on closed questions:  Locked for X days. Comments on this question have been disabled, but it is still accepting [votes and] other interactions.  Or, as others have suggested, the additional &quot;but it is still accepting [...]&quot; part can simply be removed as it hardly provides any new information. Consider this example from the Rogue class traits:     Trained Skills: Stealth and Thievery. From the class skills list below, choose four more trained skills at 1st level.   &nbsp;&nbsp;&nbsp;&nbsp;Class Skills: Acrobatics (Dex), Athletics (Str), Bluff (Cha), Dungeoneering (Wis), Insight (Wis), Intimidate (Cha), Perception (Wis), Stealth (Dex), Streetwise (Cha), Thievery (Dex)   The Rogue is trained in Stealth and Thievery. However, they're also included in the Class Skills section, and it invites you to: 'choose four more trained skills' from that list. This seems to be similar for all the classes.  So can you train Stealth and Thievery as a choice as well have it initially trained or the equivalent for other classes? How many ways to arrange people on a bench so that no woman sits next to another woman? I came across a phrase for a type of question which is designed to discover someone's religious background, particularly in the context of sectarianism and divided societies but can't for the life of me remember it.   For example, if you are in Scotland and I ask you what football team you support, that may reveal your religion. Or in N.Ireland, if I ask what school you attend, likewise that may do the same.  It's like a 'veiled question' only that's not the term I'm looking for. Any help appreciated.  I've a feeling that the second part of the phrase is (question) as in, a INSERT TERM question, but not 100% sure. How can I take a photo with everything in focus with my DSLR? Can a self-complementary graph on 100 vertices have precisely one vertex of degree 50? Are collective nouns always plural, or are certain ones singular? I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved? Where does top command get all the data for CPU Utilization? Why does Ubuntu fail to run .exe files? / How do I run .exe? Sum of odd Fibonacci Numbers Trying to prove that the sum of odd-index consecutive Fibonacci numbers is the next even-index Fibonacci number. I have a gap in my proof that I cannot figure out. I know that induction would be easier and I have already done it that way, I am looking to use alpha and beta. $$\sum_{i=1}^n F_{2i-1} = F_{2n}$$  $$\begin{align*} \sum_{i=1}^n F_{2i-1}&amp;=\sum_{i=1}^1  \frac{1}{\sqrt{5}}(\alpha^{2i-1}-\beta^{2i-1})\\ &amp;=\frac{1}{\sqrt{5}}\left(\sum_{i=1}^1\alpha^{2i-1}-\sum_{i=1}^1\beta^{2i-1}\right)\\ &amp;\;\;\vdots\\ &amp;=\frac{1}{\sqrt{5}}[(\alpha^n-\beta^n)(\alpha^n+\beta^n)]\\ &amp;=\frac{1}{\sqrt{5}}(\alpha^{2n}-\beta^{2n})\\ &amp;=F_{2n} \end{align*}$$ Mobile notifications unread status independent from full site inbox and achievements I have a common scenario in app design, where I need to store an ordered list, and make the ordering easily accessible and adjustable via an application UI.    The ordering operations are simple and operate on only one item at a time - move to top, move to bottom, move up one position, or down one position.  These positioning operations may be interspersed in with typical add / edit / delete list operations.  For discussion, this is a single-user app and db store.  Because the objects can be highly complex, I'd like to avoid caching the entire list client-side, and tracking newly created objects in memory until a big save operation occurs.    I am using MS-SQL almost exclusively on these projects, and I'm wondering if there are db features, SQL features, or design patterns I should be using to better support the management of ordered lists.    My current approach is to use a DECIMAL column to store the list positions, which become fractional during the item move process.  Then I sort the list and re-generate integer positions to normalize list.  Following this operation, it's ready for another item move.   In an example implementation, I create a column named Seq for position tracking.  Once decimal place is enough for the .5 storage.   [Seq] [decimal](10, 1) NOT NULL   When an item is re-positioned in the app UI,    I UPDATE that record with new Seq value I retrieve the full table, sorted ascending by Seq and regenerate all Seq values in the table from a 1-based integer series   The new Seq value is easily calculated-    Move to top = 0 Move to bottom = MAX(Seq) + 1 Move up = subtract 1.5 from the current Seq value Move down = add 1.5 to the current Seq value   As lists get longer, updates get slower, since I'm doing N UPDATE statements, where N is the number of rows in the table, so it seems only suitable for small tables.    Is there some kind of in-built capability for managing an ordered list in SQL or MS-SQL? Is there a means to update multiple rows in one call?    A far more performant approach would be to allow more decimal places, and then position at the median of the two adjacent items, with no re-sequencing on the list.     Move to top = Min(Seq) - 1 Move to bottom = MAX(Seq) + 1 Move up = median of the 2 previous item Seq values Move down = median of the 2 following item Seq values   This approach only requires one SELECT (containing 2 rows max) and one UPDATE.    However with enough re-positions I imagine the field would run out of decimal places. For example, if I start with items at positions 10 and 11, and keep moving items down the list from position 9, they'd be given sequences of 10.5, then 10.25, then 10.125.  After 10 moves, the positions get lengthy... 10.0009765625.    UPDATE #1 - IMPROVED RE-SEQUENCING OF THE LIST  Regarding re-sequencing, I'm more caught up on row_number(), OVER, and WITH capabilities in MS-SQL.  It's nice to find that there's a much smoother way to re-sequence the list in a single UPDATE operation;  with OrderedItems as  (     select         ItemID,         Seq,         row_number() over (order by Seq asc) NewSeq     from          Items ) update OrderedItems set Seq = NewSeq How do I increase my code coverage, or why can't I cover these lines? This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How is code coverage obtained and calculated? How do I increase my coverage?  Why can't I cover these lines? Why isn't the body of my loop or conditional statement covered? How do you debug through a compressed JavaScript file? The  defines multiple padding schemes for signature generation/verification ( and ),  and encryption/decryption ( and the less safe ).   Which attacks are possible on signature generation/verification and encryption/decryption if no padding mechanisms are applied, i.e. if raw RSA is used over the plaintext or hash? If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$? Let $f$ be a measurable function on a measure space $X$ and suppose that $fg \in L^1$ for all $g\in L^q$. Must $f$ be in $L^p$, for $p$ the conjugate of $q$? If we assume that $\|fg\|_1 \leq C\|g\|_q$ for some constant $C$, this follows from the Riesz Representation theorem. But what if we aren't given that such a $C$ exists? Exact sequence of sheaves with non exact sequence of global sections Let $X$ be some topological space. By $\mathcal{F}_i$ we denote some sheaves of abelian groups on $X$. The sequence of sheaves and morphisms  $$\mathcal{F}_1\longrightarrow \mathcal{F}_2\longrightarrow \mathcal{F}_3\longrightarrow... $$ is said to be exact if for each $x\in X$ the corresponding sequence of stalks $$(\mathcal{F}_1)_x\longrightarrow (\mathcal{F}_2)_x\longrightarrow (\mathcal{F}_3)_x\longrightarrow... $$ is exact. However if the sequence of sheaves is exact than the sequence of global sections is not necessarily exact! (The most famous example is the sequence of sheaves $$0\longrightarrow\mathbb{Z}\hookrightarrow \mathcal{O}\stackrel{\exp}{\longrightarrow} \mathcal{O}^*\longrightarrow0$$ considered as sheaves on $\mathbb{C}-\{0\}$, where $\mathcal{O}$ is a sheaf of holomorphic functions, $\mathcal{O}^*$ is a sheaf of holomorphic functions with no zeros).  So, could you give me some easy examples of such phenomenon ?