Let $\{a_n\}_{n=1}^{\infty}$ be a sequence such that every subsequence has a subsequence that converges to $L$. Then, $\lim_{n \to \infty} a_n = L$.
If a sequence $(u_n)$ be such that its every subsequence has a subsequence that converges to $0$, then $\lim u_n= 0$
How will Cryptography be changed by Quantum Computing? I realise this isn't a 'yes or no' question, and I apologise for asking something that could be seen as a discussion thread, but I had to ask.  I'm currently doing an EPQ in CS (specifically how QC will change Cryptography). I'm trying to gather up topics to cover, and so far I've scribbled down -  Effects -   National security, classical cryptographic methods (RSA, DSA, AES-256). Including Shor's algorithm. Communications Online services, e.g. BitCoin.   How would we counter this (not sure how better to phrase this) -   Lattice-based Multivariate Hash-based signatures Code-based cryptography   Is there anything else you'd recommend me including (as well as the above), or anything in the above you don't think I should include?   Honestly, the list above is a rough, first draft the main bulk of it... so don't it as gospel.  Best regards,  Cameron. Importing a material from blender to unity Cannot install vim I am running Ubuntu 11.10, as Xubuntu, in an AMD 64 pc, configured as dual boot with Windows 7.  I tried installing vim with this:  sudo apt-get install vim   I got this error message:  The following packages have unmet dependencies:  vim : Depends: vim-common (= 2:7.3.154+hg~74503f6ee649-2ubuntu2) but 2:7.3.154+hg~74503f6ee649-2ubuntu3 is to be installed E: Unable to correct problems, you have held broken packages.   I only have a very faint idea of what the problem is, and none whatsoever on how to correct this. Hope you guys can help. Story where someone gets disconnected from computers for cybercrime I read a short (in the range of 5-20 pages) science fiction story a while ago, and can't remember the title of the story or its author at the moment.  The basic story is that of a super-savvy computer hacker who got all of his knowledge of computers removed from his brain, temporarily (one year?) for cybercrime, including (IIRC) some form of identity theft, and is released into the public without any jail-time or anything. This is very hard on him, for this future-Earth relies heavily on highly interconnected computers for basic and daily needs. This is not immediately clear at the start of the story, but it becomes apparent after a little while.  Part of the story includes the main character (I don't remember if he is granted a name in the story) wanders into a cafe or a bar, and is invited to play a game of digital, . He has to turn down the invite, though, because he doesn't know and is blocked from knowing how to use computers. He also really doesn't want the other characters to know this, because apparently having your computer knowledge removed from your brain for cybercrime is a major stigma in that society. The character also has difficulty using his (futuristic equivalent of a) credit card, as that also requires some computer knowledge.  Any ideas? In the Wikipedia article , it says     After Newtonian gravitation was found to be inconsistent with special relativity, . . .   I don't see how Newtonian gravitation itself is inconsistent with special relativity.  After all, Newton's Universal Law of Gravitation is completley analogous to Coulomb's Law, so it would seem that, if there were an analogous "gravitational magnetic field", one could formulate a theory of gravitation in exact analogy with Maxwell's Theory of Electromagnetism, and of course, this would automatically be consistent with Special Relativity.  What about this approach to gravitation does not work?  The only problem I could see with this is the lack of evidence for a "gravitational magnetic field".  That being said, gravity is "weak" as it is, and my guess is that it would be extremely difficult to set up an experiment in which a massive body were moving fast enough for this "magnetic field effect" to be obsevable.  EDIT:  As has been pointed out to me in the answers, Newton itself is inconsistent with SR.  Similarly, however, so is Coulomb's Law, yet, electromagnetism is still consistent with SR.  Thus, how do we know that it is not the case that Newton's Law is the special "static" case of a more general gravitomagnetic theory exactly analogous to Maxwell's Theory:  Let $\mathbf{G}$ be the gravitation field, let $\rho$ be the mass density, and $\mathbf{J}$ be the mass current density, let $\gamma _0$ be defined so that $\frac{1}{4\pi \gamma _0}=G$, the Universal Gravitation Constant, let $\nu _0$ be defined so that $\frac{1}{\sqrt{\gamma _0\nu _0}}=c$, and suppose there exists a field $\mathbf{M}$, the gravitomagnetic field, so that the following equations hold: $$ \vec{\nabla}\cdot \mathbf{G}=-\frac{\rho}{\gamma _0} $$ $$ \vec{\nabla}\cdot \mathbf{M}=0 $$ $$ \vec{\nabla}\times \mathbf{G}=-\frac{\partial \mathbf{M}}{\partial t} $$ $$ \vec{\nabla}\times \mathbf{M}=\nu _0\mathbf{J}+\gamma _0\nu _0\frac{\partial \mathbf{G}}{\partial t} $$ where theses fields would produce on a mass $m$ moving with velocity $\mathbf{v}$ in our inertial frame the Lorentz force $\mathbf{F}=m\left( \mathbf{G}+\mathbf{v}\times \mathbf{M}\right)$.  This theory would automatically be consistent with SR and would reduce to Newton's Law of Gravitation for the case of gravitostatics:  $\frac{\partial \mathbf{G}}{\partial t}=\frac{\partial \mathbf{M}}{\partial t}=\mathbf{J}=0$.  (To be clear, you can't just set the time derivatives equal to $\mathbf{0}$ as it seems I have done.  Upon doing so, you obtain the corresponding static theory, which is technically incorrect (as you can easily see because it won't be relativistically invariant), but is nevertheless often a useful approximation.)  My question can thus be phrased as:  without appealing directly to GR, what is wrong with this theory? There does not exist group $G$ such that Aut$(G)\cong \mathbb{Z}_n$ (for odd $n$) Take a look at the following picture:   Why does the light at the bottom of the water form this pattern? I have also seen the same phenomenon in all the swimming pools I've ever visited, of whatever depth they may be. How does this happen? Error - SqlDateTime overflow. Must be between 1/1/1753 12:00:00 AM and 12/31/9999 11:59:59 PM In the late 1970s I bought a book at a school book fair (likely published by Scholastic) about a young boy who lived on a generational starship.  The ship was failing.  I remember some bit about an icey cold airlock.  One of the constellations (Cygnus) somehow took on actual fleshy form and manifested as a talking swan, which somehow helped the starships reach their destination.  Pointers? Why are the shebang parts of the following elementary scripts not working:  $ cat hello.sh #! /bin/sh echo Hello $ ./hello.sh bash: ./hello.sh: /bin/sh^M: bad interpreter: No such file or directory  $ cat hello.py #! /usr/bin/env python3 print("Hello") $ ./hello.py : No such file or directory   whereas calling the interpreter manually is working:  $ sh hello.sh Hello $ python3 hello.py Hello Why do light disappears the moment we switch off the source (inside the wooden box)? How to jusify {e,n} is a valid RSA public key? How to validate an email address using a regular expression? How to turn off notifications for individual apps? sum of polynoms of given property Using INSERT INTO...EXEC AT linked server into temp table fails with Msg 7391 How to handle calendar TimeZones using Java? I have a Timestamp value that comes from my application. The user can be in any given local TimeZone.  Since this date is used for a WebService that assumes the time given is always in GMT, I have a need to convert the user's parameter from say (EST) to (GMT). Here's the kicker: The user is oblivious to his TZ. He enters the creation date that he wants to send to the WS, so what I need is:  User enters: 5/1/2008 6:12 PM (EST)  The parameter to the WS needs to be: 5/1/2008 6:12 PM (GMT)  I know TimeStamps are always supposed to be in GMT by default, but when sending the parameter, even though I created my Calendar from the TS (which is supposed to be in GMT), the hours are always off unless the user is in GMT. What am I missing?  Timestamp issuedDate = (Timestamp) getACPValue(inputs_, "issuedDate"); Calendar issueDate = convertTimestampToJavaCalendar(issuedDate); ... private static java.util.Calendar convertTimestampToJavaCalendar(Timestamp ts_) {   java.util.Calendar cal = java.util.Calendar.getInstance(       GMT_TIMEZONE, EN_US_LOCALE);   cal.setTimeInMillis(ts_.getTime());   return cal; }   With the previous Code, this is what I get as a result (Short Format for easy reading):  [May 1, 2008 11:12 PM] I'm planning on re-watching the currently-released 5 Marvel films prior to seeing The Avengers.  Have Marvel released any sort of official viewing order?  Captain America: The First Avenger seems like the hardest one for me to place in order with the rest.  It takes place prior to the other films, but has the greatest number of references to the other films.  So should it be watched first, or last?  The rest of them are relatively clear, as they're chronological in the order they're released, with the possible exception of The Incredible Hulk and Iron Man 2 happening at the same time. Where can I find legendary crafting materials? Apart from testing it myself, I've seen a few posts  and , including from Sketchup users like me, sort of circle around this topic but never ask this question directly. How can I overcome these problems in DupliGroups or Collection Instances?  moving its origin seems to require moving to World origin (and using up a layer for clarity) &lt;=&gt; linked meshes have their own local origin which I can move data around in Edit Mode (easy enough)  It is impractical to link up DupliGroup data to previously created meshes because the origin mismatch as above, and the mesh data that remains in it and needs to be deleted somehow  Linked meshes don't have the above two problems (can be 'blocked in' and then detailed up all at once) but I can't add objects to them, only faces. Say I'd like to add handles as linked meshes, because handles are used elsewhere in the model too.    How feasible would it be to make a linked object type with deeper hierarchy? Say an object that would look at its children and simply make every other instance have the same children. It would also mean dragging and dropping in outliner would be the simplest way to manage it by the looks of it.