As far as I understand, the Heisenberg uncertainty principle states that the more one of the conjugate quantities are known, the less the other is known. So for instance, if the velocity of a particle is known more precisely, its location will become known less precisely.  I also read somewhere that it's because if you direct some ray at the moving particle, the ray will reflect, giving the former position of the particle, but the whole collision between the ray and the particle changes the particle's momentum, thus only one can be measured at a time which is the Heisenberg uncertainty principle.  In that case, if there is an indefinitely precise measuring device that can detect the particle's position and velocity at the same time, can the Heisenberg uncertainty principle disproved? Also, does the Heisenberg uncertainty principle apply only to subatomic particles, or large objects too?
From what I understand, the  states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon.  However, isn't this just an observational limit? There is a definite velocity and momentum, we just don't know it. As in, we can only know so much about the universe, but the universe still has definite characteristics.  Considering this, how do a wide range of quantum mechanical phenomena work? For example, quantum tunneling - its based on the fact that the position of the object is indefinite. But the position is definite, we just don't know it definitely. Or the famous light slot experiment? The creation of more light slots due to uncertainty of the photon's positions?  What I am basically asking is why is a limit on the observer, affecting the phenomenon he is observing? Isn't that equivalent to saying  because we haven't seen Star X, it doesn't exist? It's limiting the definition of the universe to the limits of our observation!
Let $been(x,y)$ denote "person x has been to place y."   Express “Every person has been to 2 or more places” using quantifiers and $been(x, y)$.  This one is completely stumping me. I'm sure that I haven't come across this kind of concept before, and can't wrap my head around how I would approach it. I suspect the quantifiers should be $∀x$, $∀y$, and that it may involve negating the statement "every person has been to one or zero places," but that's as far as I can manage to go. Any help greatly appreciated. Counterexample for the normalizer being a normal subgroup Can I deduct a contribution to a traditional IRA if I am also contributing to a 401(k) in the same tax year? sudo credential caching on by default How best to include other scripts? The way you would normally include a script is with "source"  eg:  main.sh:  #!/bin/bash  source incl.sh  echo "The main script"   incl.sh:  echo "The included script"   The output of executing "./main.sh" is:  The included script The main script   ... Now, if you attempt to execute that shell script from another location, it can't find the include unless it's in your path.  What's a good way to ensure that your script can find the include script, especially if for instance, the script needs to be portable? Changing footnote symbols Why does Windows only show about 3.5 GB of my 4 GB of RAM? I recently upgraded my computer's RAM to 4&nbsp;GB. My 32-bit Windows installation shows only 3574&nbsp;MB of the memory. How can I make Windows use the full amount of RAM? Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$) This is one of the BibTex entries giving the problem:  @ARTICLE{2015ApJ...808L..36B,    author = {{Bonnivard}, V. and {Combet}, C. and {Maurin}, D. and {Geringer-Sameth}, A. and      {Koushiappas}, S.~M. and {Walker}, M.~G. and {Mateo}, M. and      {Olszewski}, E.~W. and {Bailey}, III, J.~I.},     title = "{Dark Matter Annihilation and Decay Profiles for the Reticulum II Dwarf Spheroidal Galaxy}",   journal = {\apjl}, archivePrefix = "arXiv",    eprint = {1504.03309},  primaryClass = "astro-ph.HE",  keywords = {dark matter, galaxies: dwarf, galaxies: individual: Reticulum II, gamma rays: galaxies, methods: statistical, stars: kinematics and dynamics},      year = 2015,     month = aug,    volume = 808,       eid = {L36},     pages = {L36},       doi = {10.1088/2041-8205/808/2/L36},    adsurl = {http://adsabs.harvard.edu/abs/2015ApJ...808L..36B},   adsnote = {Provided by the SAO/NASA Astrophysics Data System} }   and corresponding bbl file giving the error at compilation is  \bibitem{2009ApJ...697.1071A} {\sc W.~B. {Atwood}, A.~A. {Abdo}, M.~{Ackermann}, W.~{Althouse},   B.~{Anderson}, M.~{Axelsson}, L.~{Baldini}, J.~{Ballet}, D.~L. {Band},   G.~{Barbiellini}, and et~al.} \newblock {\bf {The Large Area Telescope on the Fermi Gamma-Ray Space Telescope   Mission}}. \newblock {\em \apj}, {\bf 697}:1071--1102, June 2009.   My guess is that Kile doesn't like references of the form 2015ApJ...808L..36B since these are the only ones giving the error.    Can somebody hint me to the problem in this? Thank you very much I have a 10 stock portfolio and considering market conditions that are on the rise when this question in being asked, a few of them did hit their 52-week high price.  I would like to call myself a long term investor and I do not like to trade so much. If I take "Buy low sell high" as gospel then this is in my opinion a good selling position.  On one hand, I think I should lock my profit because stocks don't hit a 52-week high every day, but on the other hand, there is nothing wrong with the company and it is very well positioned to go up even further.  Any suggestions? Internet through wireless hotspot, intranet through wired network - can I use both at the same time? I have been tring this for a while now, without success. I have read online this can be done, either by changing the default gateway (DG) or messing with the DG's metric  The short story is: I need to connect to my company's ERP system (port 80 for some web services and port 22 for sftp and bash) with using my notebook computer's LAN card - but I can't connect to the Internet on this network. So I have my mobile phone's 3g hotspot when I need to go online. But I want to use both at the same time without so much as opening another web browser process.  At the moment, I am using the ERP system regularly - and whenever I need to go online to check a mail or research something related to work, I need to unplug the network cable so the wifi can kick in... which is starting to become annoying especially if I am connected to the ERP system using FTP (Filezilla) or Shell (putty)  Can someone help me with the configurations?  Below are some of the details I can provide:  Wired network - office LAN - for connection to the ERP system: DHCP -    Yes IPv4      10.64.200.245 Subnet    255.255.240.0 DG        10.64.193.254 DHCP Serv 10.64.17.191 DNS       10.68.72.200           10.68.20.200 WINS      10.68.77.200           10.64.20.200   Below are the details for my WiFi internet connection - over my mobile hotspot  DHCP      Yes IPv4      192.168.43.39 &lt;- I'm guessing this changes every time I restart the wifi subnet    255.255.255.0 DG        192.168.43.1 DHCP      192.168.43.1 DNS       192.168.43.1   Finally, here is the tracert results (btw, I'm on Windows 7, 64bit and the remote system should be on Linux) - the target ERP ip address is 10.76.142.39  Tracing route to 10.76.142.39 over a maximum of ...    1    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.64.193.253   2    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.64.4.13   3    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.76.23.124   4     1 ms    &lt;1 ms    &lt;1 ms  10.76.23.93   5     1 ms    &lt;1 ms    &lt;1 ms  2xx-xx-xx-9.adsl...   6     1 ms     1 ms     1 ms  2xx-xx-xx-9.adsl...   7     1 ms     1 ms     1 ms  2xx-xx-xx-10.adsl..   8     2 ms     1 ms     2 ms  10.76.135.125   9     1 ms     1 ms     1 ms  10.76.142.39   sorry, I had to mask out some details above... wasn't sure if they would have any confidentiality issues.  Any help is much appreciated. external variable in awk Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F Let $X$ be a $T_1$-space, and show that $X$ is normal if and only if each neighbourhood of a closed set $F$ contains the closure of some neighbourhood of $F$.  I saw this statement in the book Introduction to topology and modern analysis by Simmons. I tried to prove it but I did not get any where. How may it be proved? Is there a keyboard shortcut to "unselect" in Windows Explorer? If I've got a file (or files) selected in Windows Explorer, the only way I've found to "unselect" them is click with the mouse on some empty space.  I thought Esc would do this, but it doesn't. Also changing focus with Tab or Shift + Tab doesn't work; the file(s) are still selected even if focus goes to the address bar for instance.  Does anyone know of a keyboard shortcut to do this? I have this problem: I'm used to compile and run .c files with CodeBlocks. If I do that from my Desktop (ext4 partition) it works without problems, but doing this from my secondary hard drive (NTFS partition) makes CodeBlocks to say permission denied while running a .c file.  I have read it's because of the partition type is it correct? But I don't know how to solve it. I tried to edit fstab (sudo gedit /etc/fstab) adding this line:   /dev/sda /media/Dati ntfs user,exec 0 1   but after rebooting Ubuntu I had a warning on boot about a problem mounting a drive, that's because I set KDE to auto mount my Dati drive on boot.   So I should auto mount my NTFS drive with execute permission? How can I do that? I have  with a bounty that will expire in a few days. It looks like nobody will get the bounty; only one answer was posted during the bounty period, and it has no upvotes.  In cases like this, the bounty is thrown away.  Why isn't it refunded instead, if no answerer has earned it? Where do I find the client id and client secret of an existing connected app? How to auto close LWC quick action from JavaScript? This has been a old live-action movie from Asia, most likely Japan. I've seen it some time in the late 80's and I think it's been black/white only.  Earth is invaded by UFOs (small and round, like flying balls), coming from Mars.  Japan (I think) built some kind of super spaceship, initially hidden within some secret port in some kind of island/mountain.  The spaceship looks similar to a classic battleship, but with an added drill below the front.  In the movie's finale it's revealed that this is some kind of   super weapon/bomb that has to be manually piloted by someone. When launched it starts rotating and flies (formed like a bullet but with the drill/corkscrew head).   To defend Earth, the ship is sent on a mission to Venus, where the UFOs seem to originate. I don't remember the specific reason or conclusion here.  The ship starts underwater or launches from the mountain on the island, then taking off and fighting UFOs while leaving Earth's atmosphere. Math people:  The title is the question. I am convinced that uncountable sets exist, thanks to Cantor's diagonal proof.  It is not intuitively clear to me that uncountable ordinals or cardinals should exist.  What axioms of set theory are needed to accept their existence?  I think I have read here that the Axiom of Choice is not necessary.  I am reluctant to accept as "true" any theorems that rely on the Axiom of Choice.  EDIT: This question may be a duplicate: I just found  .  I apologize if this is so.