Can we construct a divergent sequence where the difference between consecutive terms is less than epsilon for $n \geq N$?
Does an increasing sequence of reals converge if the difference of consecutive terms approaches zero?
Wikipedia lists the following pseudocode for HMAC:  function hmac (key, message)     if (length(key) &gt; blocksize) then         key = hash(key) // keys longer than blocksize are shortened     end if     if (length(key) &lt; blocksize) then         // keys shorter than blocksize are zero-padded ('∥' is concatenation)          key = key ∥ [0x00 * (blocksize - length(key))]      end if      // Where blocksize is that of the underlying hash function        o_key_pad = [0x5c * blocksize] ⊕ key      // Where ⊕ is exclusive or (XOR)     i_key_pad = [0x36 * blocksize] ⊕ key       // Where '∥' is concatenation        return hash(o_key_pad ∥ hash(i_key_pad ∥ message))  end function   Why are they there?  How were they chosen?  It seems to me that  $hash(key + hash(message))$ (where + is concatenation) would suffice.    Obviously I'm missing something.  What is it? How do I install additional drivers? I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related: When upgrading to Ubuntu 14.04 from Ubuntu 12.04 I am getting the following error:     W:Failed to fetch    Unable to find expected entry 'non-free/source/Sources' in Release   file (Wrong sources.list entry or malformed file) , E:Some index files   failed to download. They have been ignored, or old ones used instead. Force alt + tab to switch only on current workspace in GNOME shell I am looking for a clean and fast method to force GNOME in Ubuntu 14.04 to switch between active apps only on the current workspace when pressing the shortcut alt + tab. What was the galaxy formation Rust saw before confronting Erol Childress in  S01E08?  It was weird like out of the series. I guess it was some sort of hallucination, a product of Rust's madness or addiction. Problem in skew-symmetric matrix Let $A$ be a real skew-symmetric matrix. Prove that $I+A$ is non-singular, where $I$ is the identity matrix. 2D inhomogeneous biharmonic equation Why didn't Gollum grow old and die after he lost the One Ring to Bilbo? How to install qt 4.8 from repository? Command "find -name" must be enclosed in quotes or it doesn't work. Why is that? Google isn't surfacing Events rich snippets in SERP when JSON-LD Structured Data is valid Google confirms our site has thousands of valid MusicEvent structured data objects presented using JSON-LD, as indicated in the Structured Data section of Webmaster Tools. However, rich snippets for the events do not show up in any search result pages. The Rich Cards tab in Webmaster Tools says:     We did not find any structured data for rich cards on your website.   The structured data is valid with no errors in the Structured Data Testing Tool. We do generate some warnings occasionally for missing endDate and price fields. Comparing our code to a survey of other sites whose rich snippets do appear, we are not doing anything unique in terms of our markup.  The data has been there for months, in fact over the months we've tried also using Microdata format. The Structured Data section indicates that many pages were crawled this week.  Besides SDTT validation, what else can I check to troubleshoot this issue? Is two-thirds plural? Is 2/3 always, sometimes or never plural?  E.g.     1a) 2/3 of the pizza were eaten.     1b) 2/3 of the pizza was eaten.      2a) 2/3 of the visitors were men.     2b) 2/3 of the visitors was men.   I feel that example 1 could go either way but example 2b sounds very wrong.  Is there a rule for this? I don't see advantages of using events over delegates, other than being syntactical sugar. Perhaps I am misunderstanding, but it seems that event is just a placeholder for delegate.  Would you explain to me the differences and when to use which?  What are the advantages and disadvantages? Our code is heavily rooted with events, and I want to get to the bottom of it.  When would you use delegates over events and vice versa? Please state your real world experience with both, say in the production code. $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors How to know the model has started overfitting? Prove the Radical of an Ideal is an Ideal I am given that $R$ is a commutative ring, $A$ is an ideal of $R$, and $N(A)=\{x\in R\,|\,x^n\in A$ for some $n\}$.  I am studying with a group for our comprehensive exam and this problem has us stuck for two reasons.  FIRST - We decided to assume $n\in\mathbb{Z}^+$ even though this restriction was not given. We decided $n\ne 0$ because then $x^0=1$ and we are not guaranteed unity. We also decided $n\notin\mathbb{Z}^-$ because $x^{-1}$ has no meaning if there are no multiplicative inverses. Is this a valid argument?  SECOND - We want to assume $x,\,y\in N(A)$ which means $x^m,\,y^n\in A$ and use the binomial theorem to expand $(x-y)^n$ which we have already proved is valid in a commutative ring and show that each term is in A so $x-y$ is in $N(A)$. The biggest problem is how to approach the $-y$ if we are not guaranteed unity. Does anyone have any suggestions?  Thank you in advance for any insight. How to debug suspend? Why is the cone measurable? Problem Denote by $\lambda_n$ the Lebesgue measure on $\mathbb {R}^n$. Let $h \in \mathbb {R}_{&gt;0}$. Let $A \subset \mathbb {R}^{n-1}$ be Lebesgue-measurable with finite measure. Define the cone $C(A,h)$ as the union of all straight lines connecting a point in $A \times\{0\}$ with the point $(0, h) \in \mathbb {R}^{n-1} \times \mathbb{R}$. Prove that $\lambda_n (C(A,h))=\frac{h}{n}\cdot \lambda_{n-1}(A)$. Where I struggle  Assuming that $C(A,h)$ is (Lebesgue-)measurable, this is a simple application of Fubini. How Fubini is used is all clear to me.  However, why is $C(A,h)$ measurable? It seems one could roughly argue as follows: As $A$ and $[0,h]$  are measurable so is $A \times [0,h]$. As $A \times [0,h]$ is measurable it is the union of a null set and a Borel set. $C(A,h)$ is the image of $A \times [0,h]$ under a certain diffeomorphism (c.f. ). Diffeomorphisms map null sets to null sets, and Borel sets to Borel sets. Hence, $C(A,h)$ is (as a finite union of measurable sets) measurable.  Unfortunately, I am not allowed to use the above properties of diffeomorphisms. What are other ways to prove the claim? Please only give a hint to set me thinking. Why I cannot ping 192.168.0.108 (my computer IP?) Booting Ubuntu Failure : error: attempt to read or write outside of disk 'hd0' I have installed Ubuntu 12.10 in a Western Digital external hard drive (320GB). This is a complete installation, not a live USB.  When I plug it in my HP desktop I go to the BIOS settings and boot off the hard drive, everything work perfectly as it should. Now this works on every single computer and laptop in my house (all HP), except for ONE. My HP ProBook 4530s.  When I select to boot of the USB I get the message:  error: attempt to read or write outside of disk 'hd0'   Now, I have removed the hard drive from my laptop and the external drive is the ONLY drive plugged in. Below is a screenshot of the message on the screen. After the message I navigate to ls / (as shown below):    After here I try to acces other folders under ls /, for example, I try to go to ls /boot to get to the grub folder. Then I get the same message as before: as shown below:    grub rescue&gt; ls /boot  error: attempt to read or write outside of disk 'hd0' grub rescue&gt; _   The only folders I can access without getting the message again are /home, /run and /usr.   So how do I:   Boot Ubuntu from GRUB2 (this screen) manually Set to automatically boot Ubuntu If possible an explanation for this problem   Thanks!