Hello I want to move from my compact camera to a dslr. I am fan of landscape photos so I want to buy an ultra-zoom lens. My camera supports 14x optical zoom. I know that for compact cameras it's just a notation, so searching further from the official website:   focal-length = 5.0 – 70.0 mm (35 mm equivalent: 28 – 392 mm)   I cannot understand what 35mm equivalent means. I want to buy lens that has 55-200 focal length. So will the new lens have better zoom or not?  I don't provide any model because I believe it's better for the question not be a comparison between certain products.
What is the rule to convert the 'mm' notation to the 'optical zoom' notation? I searched a bit and found this one:  optical zoom = maximum focal length / minimum focal length   For example a 18-55mm lens would have a 3x optical zoom, and a 18-200mm lens would have a 11x optical zoom. Is that right?
Internal or external oscillator I always use the internal oscillator that pics have as I have never found the need to run anything at higher frequency than 8 MHz (which is the fastest the pics I use tend to be able to go). Are there any reasons, beyond going above 8 MHz, that mean I should use an external oscillator? It just seems like one more thing to go wrong to me but I'd be interested to hear what others do. jQuery Datepicker with text input that doesn't allow user input How to force a table into page width? Why was the Triwizard cup portkey in Goblet of Fire two-way? At the end of the scene in the cemetery in GoF, the spirits who emerged from Voldemort's wand tell Harry to go grab the trophy (which, of course, was a portkey that took Harry and Cedric from the maze to the cemetery), and that the trophy portkey would take Harry back to Hogwarts.  Why would the portkey do that?  Are all the portkeys 2-way?  If possible, I would prefer as much of the answer based on canon (or JKR) as feasible Let $K\subseteq \mathbb{R}^{n} \times \{ 0 \}\subseteq \mathbb{R}^{n+1} $ and $v=(0,0,\cdots,1) \in \mathbb{R}^{n+1}$.      For every $x \in K$,  let $$Lx=\left \{ tv+(1-t)x \; | \ t \in [0,1] \right \}$$      Define    $$ \text{Cone}(K)=\bigcup_{x \in K}Lx. $$   namely the union of all segments from $v$ to every point of $K$.      According to all definitions that I see on books, Cone is defined:       However the exercise I'm working on  asks to find under what circumstances  $$\text{Cone}(K)=\bigcup_{x \in K}Lx$$ is isomorphic to $(K \times [0,1]) /(K \times \{ 1 \})$ (quotient space).   For example if $$K=\{(1/n,0):n\in\mathbb{N}\} \cup (0,0)$$ I can see both of sets form the same graph but I'm still unable to derive a homeomorphism between these two objets. Prove that : $\displaystyle \lim_{n\to \infty} \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{2n}=\ln 2$    the only thing I could think of is that it can be written like this :  $$ \lim_{n\to \infty} \sum_{k=1}^n \frac{1}{k+n} =\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{1}{\frac{k}{n}+1}=\int_0^1 \frac{1}{x+1} \ \mathrm{d}x=\ln 2$$  is my answer right ? and are there any other method ?(I'm sure there are) If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? The probability of a photon having just the right amount of energy for an atomic transition is $0$. Calculate the limit of two interrelated sequences? I'm given two sequences:  $$a_{n+1}=\frac{1+a_n+a_nb_n}{b_n},b_{n+1}=\frac{1+b_n+a_nb_n}{a_n}$$  as well as an initial condition $a_1=1$, $b_1=2$, and am told to find: $\displaystyle \lim_{n\to\infty}{a_n}$.  Given that I'm not even sure how to approach this problem, I tried anyway. I substituted $b_{n-1}$ for $b_n$ to begin the search for a pattern. This eventually reduced to:  $$a_{n+1}=\frac{a_{n-1}(a_n+1)+a_n(1+b_{n-1}+a_{n-1}b_{n-1})}{1+b_{n-1}+a_{n-1}b_{n-1}}$$  Seeing no pattern, I did the same once more:  $$a_{n+1}=\frac{a_{n-2}a_{n-1}(a_n+1)+a_n\left(a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})\right)}{a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})}$$  While this equation is atrocious, it actually reveals somewhat of a pattern. I can sort of see one emerging - though I'm unsure how I would actually express that. My goal here is generally to find a closed form for the $a_n$ equation, then take the limit of it.  How should I approach this problem? I'm totally lost as is. Any pointers would be very much appreciated!  Edit:  While there is a way to prove that $\displaystyle\lim_{n\to\infty}{a_n}=5$ using $\displaystyle f(x)=\frac{1}{x-1}$, I'm still looking for a way to find the absolute form of the limit, $\displaystyle\frac{1+2a+ab}{b-a}$. What is the definition of a timelike and spacelike singularity? Groups in derived series are normal in the whole group I am considering a finitely generated, solvable group $G$ which has subexponential growth. Let $G=G_0\vartriangleright G_1\vartriangleright....\vartriangleright G_d\vartriangleright G_{d+1}=1$ denote the derived series of G.  It should be the case that $G_d$ is normal in $G$. Does anyone know why this is true? I don't know whether all of the assumptions above are necessary for the result. Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$? stab(S) is isomorphic to $ S_k \times S_{n-k} $ Show that the group $S_n$ (right) acts on the set of subsets of $\{1,2,\ldots n\}$ by $\rho(S,\sigma)=S\sigma$. Show that there are $n+1$ orbits, one for each possible value of $|S|$. Show that if $|S|=k$ then $\mathrm{Stab}(S)\cong S_k\times S_{n-k}$.  I have shown that there are n+1 orbits but now I am stuck with the last bit. my initial thought is that if I let $S =\{1,2,3,...,k\}$ then $\mathrm{Stab}(S)$ would involve $(1)(2)(3)...(k)$ i.e. mapping to itself and then $k+1$ to $n$ mapped in any ways ($S_{n-k}$) I feel like $\mathrm{Stab}$ is isomorphic to $S_{n-k}$ what am I misunderstanding here? How would I prove the last part? Thanks a lot Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$ Short story about a man stranded on a red planet with a sentient hand as his friend I remember reading a short story 10 to 15 years ago about a man stranded alone on a red planet, where nothing would be green, and so he would miss that color. There was a sentient hand to keep him company, and it talked to him. I don't remember if the hand was a native life form or his own hallucination.  The story was not very old at that time, so it may have been written in the late 90s or 00s. In a tennis tournement of 128 players, elimination system, what is the probability that two twins will meet at some point? Why does my shell script choke on whitespace or other special characters? Motivation: I once had one surplus card on my hand, and knew the robbers would come soon. So I gave it to someone for free, to avoid losing more cards when they hit. I was surprised by how badly this was received. Two of the three other players (the hosts of the game) acted upset, like I had tried to cheat. I had to take the card back, get robbed the next turn and 'giving cards away for free' was banned immediately. (Oh, how I hate mid-game additions to the rules. But that's beside the point.)  So now the question: Is this really illegal in Settlers of Catan? Is it generally considered underhanded in any way? If so, why?   My reasoning was like this:        Consider players A and B.   A wants to give B a sheep.   A trades a sheep and one rock to B, in exchange for wheat.   A trades the received wheat for the (formerly his) rock.   A and B now both have the same resources they had in the beginning, only the sheep has moved from A to B. Does a percentage require a singular or plural verb, for example, do we say ten percent "go" or "goes"? Mac-like alt-tab replacement for Windows 7? Is there an alt-tab replacement for Windows 7 that works in the same manner as command-tab and command-tick (tilde) on OS X?  Requirements:  1. Completely keyboard-shortcut-based, no mouse action should be necessary.  2. 2 keyboard shortcuts with the following behavior:  a.) alt+tab:       cycles through open applications (NOT windows... applications, meaning even if i have 10 firefox windows open, I only want to see firefox once in the list that comes up when i hit this shortcut)  b.) alt+`:     cycles through WINDOWS that are instances of the currently active application (meaning if firefox is my active window and i hit shortcut2, it will cycle through those 10 firefox windows, while ignoring any other windows from ANY other application).    Update 08:40 5/21: I tried out eidylon's suggestion, TopDesk.  It doesn't provide any of the functionality described here.  Other apps I've already tried:   VistaSwitcher Switcher Dexpot (awesome app, still using, but doesn't do what I want in this case... also looked for plugins but couldn't find one that does it) UltraMon Nvidia nView   update: Unfortunately I still haven't found a solution for this.  update: made this a community wiki in case anyone is ever able to find a solution for this. How can I enable AHCI on a SATA drive after installing Windows? Can I enable AHCI after installing Windows 7 in a SATA drive that was on IDE mode?