Is the infinite intersection of finite sets a finite set? Could you give me some examples or counterexamples?
I know that there are questions asking like "intersection of a infinite collection of sets" and I can understand that the answer for that one is a null set, but I got a question here, in which all sets are finite and nonempty. Please take a look at the pic below.  It's a True/False question.  What I'm confused about is that the "infinity" sign in the interception. Since all sets are finite, does it mean that there are many sets in the chain are the same? (because the symbol used is for subsets not for proper subsets). Please give me some hints how I should think about this question.  Thank you
Can an abstract class have a constructor? Can an abstract class have a constructor?  If so, how can it be used and for what purposes? How do I align an image to centre? How do I align an image to centre?  In a beamer presentation I have a 2-3 items on a slide followed by an image. The image is not wide enough to cover whole slide, so it leaves around 30% space from right. How do I adjust it to leave enough space on both sides?  \begin{frame} \frametitle{Outlook} \begin{itemize} \item apps \item apps \item apps \includegraphics[scale=0.3]{P2P}     \end{itemize} \end{frame} How can I disable the "Open File Security Warning" when I want to run downloaded executable files? How to automatically add &raquo; (») to  elements using CSS? Do photons bend spacetime or not? I have read this question:     where Safesphere says in a comment:     Actually, photons themselves don't bend spacetime. Intuitively, this is because photons can't emit gravitons, because, as any massless particles not experiencing time, photons can't decay by emitting anything. The latest theoretical results show that the gravitational field of a photon is not static, but a gravitational wave emanating from the events of the emission and absorption of the photon. Thus the spacetime is bent by the charged particles emitting or absorbing photons, but not by the photons themselves.        where John Rennie says:     as far as I know there has been no experimental evidence that light curves spacetime. We know that if GR is correct it must do, and all the experiments we've done have (so far) confirmed the predictions made by GR, so it seems very likely that light does indeed curve spacetime.   Now this cannot be right. One of them says photons do bend spacetime, since they do have stress-energy, but it is hard to measure it since the energy they carry is little compared to astronomical body's stress-energy. So they do bend spacetime, it is just that it is hard to measure it with our currently available devices.  Now the other one says that photons do not bend spacetime at all. It is only the emitting charge (fermion) that bends spacetime.  Which one is right? Do photons bend spacetime themselves because they do have stress-energy or do they not? Factorial sum estimate $\sum_{n=m+1}^\infty \frac{1}{n!} \le \frac{1}{m\cdot m!}$ Prove that:  $$\displaystyle \sum_{n=m+1}^\infty \dfrac{1}{n!} \le \dfrac{1}{m\cdot m!}$$  I have tried induction on $m$ but it does not work very well. Any suggestion? How to forbid keyboard shortcut stealing by websites in Firefox Many websites, especially everything involving rich text editing (this site is guilty as well), steal keyboard shortcuts normally used to control Firefox and make them do something else instead. It is totally infuriating when I press something like Cmd-number, Cmd-L, Cmd-T, or Cmd-K and it doesn't do what I want it to. Can I make it stop?  Actually, it would probably be for the best if I could forbid stealing of all Cmd-* shortcuts. I've never seen them used for anything useful. Is it possible? SOAP or REST for Web Services? Biasing circuit - Voltage follower circuit I am using , which is and Bias controller/sequencer. I am using this for Providing gate voltage and drain voltage to the . In the datasheet, it is mentioned that the module with combination of EVM can be used in two applications. Application Option 1: Fixed negative gate biasing with pulsed drain biasing. Application Option 2: Pulsed negative gate biasing with pulsed drain biasing. I am trying to design both applications on a single board. The second option for future use. For the 1st application option, he has mentioned a few pins as No connection and he has used those NC pins on the 2nd application.  The issue I am facing:- They have used voltage followers for providing a low impedance output path for pin number 3(GCO). I have reverse-engineered the Ckt from the below-attached image, but I am unable to identify the voltage follower they have used. Pin number 2 of the voltage follower has been connected to pin number 2 (NC/GCP) of the Module. There has been no description of this pin number. I am guessing these:-  Pin numbers 1 and 4 are connected together and output is provided through them. Pin number 5 is +Ve supply hence connected to GND(Highest +Ve supply)? Pin number 3 is connected to -8V Pin number 2 is connected to pin number 2 of MABC-001000-DP000L, which I am unable to understand.  I have mailed component manufacturer regarding full schematic, till now I haven't heard from them. Can anybody help me with this? Thanks in Advance. Low-resolution pic of EVM. I don't think it helps in any way.   Layout Image ASCII to Binary and Binary to ASCII conversion tools? Which is a good tool to convert ASCII to binary, and binary to ASCII?  I was hoping for something like:  $ echo --binary "This is a binary message" 01010100 01101000 01101001 01110011 00100000 01101001 01110011 00100000 01100001 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00100000 01101101 01100101 01110011 01110011 01100001 01100111 01100101   Or, more realistic:  $ echo "This is a binary message" | ascii2bin 01010100 01101000 01101001 01110011 00100000 01101001 01110011 00100000 01100001 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00100000 01101101 01100101 01110011 01110011 01100001 01100111 01100101   And also the reverse:  $ echo "01010100 01101000 01101001 01110011 00100000 01101001 01110011 00100000 01100001 00100000 01100010 01101001 01101110 01100001 01110010 01111001 00100000 01101101 01100101 01110011 01110011 01100001 01100111 01100101" | bin2ascii This is a binary message   PS: I'm using bash  PS2: I hope I didn't get the wrong binary Vote too old to be changed, unless post is edited Anyone seen this one yet? Vote too old to be changed, unless post is edited My vote was only a few hours old. Then I realized the answer was wrong. Updated my question and went to remove the vote. Even after updating question I still have the issue. Small issue, but frustrating.  See also: In comments, moderators have their diamonds in the OP rectangle:        And in the review (suggested edits), mods have their diamonds outside the blue OP background highlight rectangle:        Of course, it Doesn't Really Matter At All, but it is a small discrepancy (I am not saying that in the review, OP rectangles have a bigger padding). Why are there so many close votes to review and so few of the others? In the SO Review page , I see the following stats for questions awaiting review:   Close votes:  51.8k (and rising) Suggested edits: 10 (fluctuates, but rarely goes above 20) Everything else: 0 (occasionally see some if you're really lucky)   My question is: Why?  Why are there so many close votes waiting for review? Close votes should expire after four days. And even if there's a good reason for them hanging on longer (ie they're not being viewed), there surely has to be a cut-off eventually after which they can be safely dropped?  And yes, I saw , which is asking basically the same thing. But that was several months ago, and it seems that the queue has hardly moved since then. It seems to me that there's a massive backlog that will never be cleared, and apparently will never expire either. That's not good.  And on the flip side, why are there hardly ever any new user posts or low quality posts to review -- there are always new users posting things, and I recall before this new review system was launched that the list of low quality posts to review was always pretty big. [i] Susan married Ed. (RHD)   [ii] My sister got married last fall. (COCA)   Is there a passive implication in [ii]? That is, the families and so on arrange and perform the marriage ceremonies for two people, and through all this the two get married. Is this implied in the expression [ii], and not in [i]? If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian? I know that any group satisfying $x^2=1$ for all $x$ is abelian. Is the same true if $x^3=1$? I don't think it is, but I can't find a basic counterexample. Drawing on an image with TikZ Recently I have learned how to draw simple stuff with TikZ. I really like it. Now I wonder if it is possible to draw with TikZ on a image. Instead of pasting a image in Illustrator and adding some vectors to point something in the picture I would like to do it using TikZ. Is it possible?   For example, on a picture of a computer (PNG,etc) I would like to draw some arrows and labels saying "Keyboard", "Monitor", etc. I currently only have remote access to this CentOS box, I need to move /var form the primary RAID to a new set of disks that was installed with more space, My current thoughts on how to accomplish this is to temporarily mount the new RAID to /tmp/var. rsync everything from /var to /temp/var then modify the fstab to point /var at the new disks.  Here is my question. how do I delete the existing /var on the primary disks once I have the new disks mounted to that location (assuming this is even possible remotely)? Why does QgsSpatialIndex.nearestNeighbor(point, 1) sometimes return 2 lines? I'm trying to get the closest line to a point using PyQGIS in a plugin. The active code file is this:   When I request the closest line (only 1)  nearestIds = self.spIndex.nearestNeighbor(self.feat2.geometry().centroid().asPoint(),1)   I sometimes get a list with two lines and the first one is not the closest but as far as I can see the second one is. Why is this?   Does QgsSpatialIndex use only boundingboxes for lines? How do I get the real closest line always, not only most of the time? When the trace of the Frobenius homomorphism is zero? Let's consider an elliptic curve over a finite field $\mathbb F_p$.  The trace of the Frobenius homomorphism is defined as:  $$a_p=p+1-\#E(\mathbb F_p)$$  See for example .  I read that this value is zero if and only if the elliptic curve is supersingular. Unfortunately there is no proof give. So I am looking for a proof of this. (For example a good reference). Chrome: Site has updated in the background I keep getting these notifications despite not having an RT tab open. What gives?