AC in Countable Union of Countable Sets
Countable union of countable sets(ZF)
Recovery of deleted folders in home folder By accident I've removed some folders (they were empty) in my home folder. I've created a new ones but they doesn't have proper icons etc... how can I recreate them step by step? I read on  that Ubuntu will no longer use the familiar file size units we all know by now (kB, MB, GB, TB) and switch to a different IEC standard (KiB, MiB, GiB, TiB). If this is true, I would like to know what's the reasoning behind this change, and the impact (if any) this change has, especially with multiplatform applications or applications run with Wine. Get Site Collection full URL using javascript LaTeX Classes or Styles for Schedules and/or Calendars? How can we disable triggers, Validation Rules and workflow rules in salesforce org. [on off - switch] How can we disable triggers, Validation Rules and workflow rules in salesforce org.  This becomes really needed and important when we are doing data migration(data imports) in salesforce.  The way I handled this is create a custom label and include it in workflow and validation rule logic.   example - Custom label 'Disable workflow' = True then do not fire workflows.            if its False then fire workflow  But wanted to understand if there is any more efficient way to handle these scenarios. I created a bitmap with transparent background but in the Windows Picture Viewer I see the white background and even if I reopen it in Photoshop CS3. how do I make sure the white colour in bitmap is really transparent or see if contain any transparent colour? Divisibility Proof with Induction - Stuck on Induction Step I'm working on a problem that's given me the run around for about a weekend. The statement:  For all $m$ greater than or equal to $2$ and for all $n$ greater than or equal to $0$, $m - 1$ divides $m^n - 1$.  Using induction over $n$, the base step comes easy since $m^n - 1$ is $0$ when $n = 0$.  My induction hypothesis is letting $k \geq 0$ and assuming that $m - 1$ divides $m^k - 1$. In order to show that $m - 1$ divides $m^{k+1} - 1$, I obviously need to use the induction hypothesis. However, no matter where I try to use the fact that $m^k - 1 = (m-1)a$ for some $a$ in the integers, the expression $m^{k+1} - 1$ always becomes more difficult to get to $m^{k+1} - 1$ being equal to $(m-1)b$ for some $b$ in the integers.   In other words, I can't figure out any actually helpful way to apply the induction hypothesis with the goal of proving the next step.  Any help would be appreciated! I do not understand much about mine bitcoins, but I downloaded a program that is like a wallet, but I want to know how I do to mine. Has a calling GUIminder but is for windows, someone knows one that is for ubuntu? If M is a non-orientable closed connected 3 manifold prove H1(M) is an infinite group. $f:\mathbb{R}^3\to\mathbb{R}, f(rx)=r^{\alpha}f(x)$ for some $\alpha&gt;0$, $\forall x\in\mathbb{R}$, for any $r\in\mathbb{R}$, could any one tell me which of the following is true?  $1.$ If $f(x)=f(y)$ whenever $||x||=||y||=\beta&gt;0$, then $f(x)=\beta ||x||^{\alpha}$  $2.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)= ||x||^{\alpha}$  $3.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)=c||x||^{\alpha}$ for some constant $c$  $4.$ If $f(x)=f(y)$ whenever $||x||=||y||$, then $f(x)$ must be a constant function. Thank you. Accelerating electrons via microwaves In Synchrotrons I think they use microwaves to accelerate the electrons bundles that fly through-how does putting a microwave through a cavity accelerate an electron? I know that the Electric and Magnetic fields could and do have an effect on the electron, but if the radiation is moving parallel to the electron, wouldn't the force be perpendicular? Also, how exactly does the microwave radiation look in the vacuum chamber? Are the two ends constant nodes? When I look at the definition given from the Mac OS X Dictionary (I have set American English as interface language, and the dictionary used is then the New Oxford American Dictionary), I read:     the /ði/ /ð(ə)/ /ði/ [called the definite article]   adjective   1. denoting one or more people or things already mentioned or assumed to be common knowledge: what's the matter? | call the doctor | the phone rang. Compare with a.   • used to refer to a person, place, or thing that is unique: the Queen | the Mona Lisa | the Nile.   • informal denoting a disease or affliction: I've got the flu.   • (with a unit of time) the present; the current: dish of the day | man of the moment.   • informal used instead of a possessive to refer to someone with whom the speaker or person addressed is associated: I'm meeting the boss | how's the family?   • used with a surname to refer to a family or married couple: the Johnsons were not wealthy.   • used before the surname of the chief of a Scottish or Irish clan: the O'Donoghue.   I have never thought of an article as adjective. Is normally an article defined as adjective? Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$ Let $f(x) = \sqrt{x^2-3x}$ and $g(x) = x$. Calculate the following limits, showing all working.  I've done the first two -   $$\lim_{x\to0}f(x)\\ =\lim_{x\to0}\sqrt{x^2-3x}=0$$  $$\lim_{x\to-\infty}\frac{f(x)}{g(x)}\\ =\lim_{x\to-\infty}\frac{\sqrt{x^2-3x}}{x}=\sqrt{1-\frac{3}{x}}=1$$  How do I calculate this one?  $$\lim_{x\to+\infty}(f(x)-g(x))$$ Encountering a FileSystemRights value that isn't defined in enumeration How to get ObjectContext to compile? Running a caching DNS server on my LAN This is about the seemingly controversial shield to ground connection. The system is basically a body-worn intel-based computer, powered by a battery. Two USB 3.0 (or 3.1 Gen1) cables come out to a PCB that contains two USB 3.0 hub chips (). Two external cameras plug in to this usb hub PCB (one camera for each hub). So the usb hub PCB has 4 usb connectors (2 upstream and 2 downstream).  The question is, what to do with each of the usb connector shields? The main directive is USB connection robustness.  I have seen many recommendations. For example:  Recommendation 1  TI's TUSB8020B hub reference design  ties all shells directly to ground.    Intel's  also recommends to tie to ground (although this was written for USB 2.0).    Recommendation 2  TI's TUSB8020B EVM (and datasheet) connect shields together, and to ground using RC filter:    Microchip's  also ties shields together and uses an RC filter, but a 3 orders of magnitude smaller R:    Recommendation 3  Cypess  ties each shield independently to ground using either LC or L filter (chokes really):    The cameras themselves (off the shelf) use Cypress recommendation (LC to ground). The embedded computer seems to tie to ground from visual inspection and checking continuity to ground, but I'm not 100% sure (schematics are not available).  Now we face the shield dilemma with the hub PCB (which by the way currently does not have a metallic enclosure, it is a 3d printed plastic enclosure).   What is your say? Why isn't sizeof for a struct equal to the sum of sizeof of each member? Why does the sizeof operator return a size larger for a structure than the total sizes of the structure's members? 3rd iterate of a continuous function equals identity function Brace expansion not working in a script