According to , there is the "standard" model of Peano Arithmetic. This is defined as $0,1,2,...$ in the usual sense. What would be an example of a nonstandard model of Peano Arithmetic? What would a nonstandard amount of time be like?
I would like to see an explicit example of a non-trivial elementary extension of the structure $(\mathbb{N}, +, \cdot, 0, 1)$ where $\mathbb{N}$ includes zero. Most of all I am interested in countable ones.
My exterior door deadbolt has gotten stuck - it'll open with the lever but not the key. By spraying WD-40 inside the lock, I've been able to get it to work but it's very stiff. I'd like to remove the lock and inspect the inside, either to clean/lube it or replace it. But I can't figure out how to remove the lock; there's no obvious way to do this. (I'm used to seeing two screws on the inside of the deadbolt, usually under the lever arms when it's horizontal.)    How do I remove this? I can loosen the cover plate on the inside but it doesn't do anything other than rotate a few degrees. How can I check if /bin/x86_64/bin/ls is a directory in a bash shell script  Here is what I tried:  #!/bin/bash  if [ $# -eq 2 ]; then     if [[ "$1" = /* ]]     then     cd ./bin/x86_64/bin/ls         if [ -d "$1" ]; then             echo "ok"             i="$1"             echo $i         else             echo "error2"             exit         fi     else         echo "error"         exit     fi fi A Polygon is inscribed in a circle $\Gamma$ A regular polygon P is inscribed in a circle $\Gamma$. Let A, B, and C, be three consecutive vertices on the polygon P, and let M be a point on the arc AC of $\Gamma$ that does not contain B. Prove that  $MA\cdot MC=MB^2-AB^2$  I inscribed the polygon P in the unit circle and let B=1. Past this, I'm not really sure how to proceed. It might be helpful to have M at 1 as well but given that the polygon would have the n-th roots of unity in it B seemed like a good choice. What would be a good way to proceed from here? Dismiss suggested edits which conflict with full edit instead of auto rejecting them Currently, once an edit by a user without full edit privilege is suggested, it can be either approved or rejected.  There is a known edge case that cause suggested edits to get auto rejected: (aka edit conflict)   User with full edit privilege click "edit" and start typing. Let's name this user Joe. Since the user from previous step did not yet send the edit, users without full edit privilege can still click the "edit" as well, oblivious to the fact someone else is editing the same post in those very seconds. Such user click "edit" too and start typing. Let's name this user Kenny. Kenny is faster than Joe: he send his edit first, creating new suggested edit. Joe is still typing. Joe finally done typing. He send his edit to its merry way oblivious to the consequences. As result of the full edit made by Joe, Kenny's suggested edit is kicked away and rejected. Boom.   This is all known and reported many times.  where the user got it hard with at least two auto rejections in short period of time. Some concrete examples: , , .  For edge case, it became pretty thick edge. This is not just minor hassle: enough rejections, and the user is banned from suggesting for a whole week: and remember we're talking here about good edits made by good users. The above used to count for the ban, but . Thanks Gilles for requesting such a change!   I know it was already suggested to lock edits and similar solutions, but I suggest whole different approach: instead of auto rejecting the suggested edit, dismiss it, i.e. cancel it like it never existed same way a bounty can be revoked by moderator.  In the edit suggestion page it will show "Dismissed" instead of Approved or Rejected maybe with a tooltip explaining what caused this. This will soften the blow from those edge cases, taking the edge out of them. :) Create taxonomy terms on the fly I have a set of surround speakers, connected to my iMac through the headphone jack. I use a switch to control what goes to the speaker set (iMac, iPod, or MacBook/aux). So that I don't have to be constantly unplugging and replugging, I leave the audio cable in the iMac's audio port. This means that when I'm listening to something from another source, I can't hear anything from the iMac unless I unplug the cable.  Is there a way to force sound to come out of the internal speakers, even if there's something in the audio out port? How often do ewoks eat sentients? In Return of the Jedi, the ewoks plan on eating Luke, Han and Chewie.     THREEPIO: I'm rather embarrassed, General Solo, but it appears you are to be the main course at a banquet in my honor.   At this point, the tribe had already met and befriended Leia, and had encountered the Imperials in the past, making it fairly likely that they knew humans were .  This raises the question of how often they ate sentients. Was it a one-off thing, to honor an extremely rare visit from a god, or was this fairly common? Rings' second isomorphism theorem I am thinking about the proof of the second isomorphism theorem, and something isn't very clear to me.   Let $R$ be a ring, $S\subset R$ a subring and $I\subset R$ an ideal. We have the natural homomorphism $f:R\rightarrow R/I$. The theorem states that $\mathrm{Im}(S)=(S+I)/I$. My question is why not simply $\mathrm{Im}(S)=S/I$?  I understand that it is not true (for starters, $S/I$ need not be a subring), but I cannot explain that to my self in a convincing way. Is "forte" pronounced "fort" or "for-tay"? I've always heard people say something like     "Pronunciation is not my [for-tay]"   ... but I feel that I've heard that the correct pronunciation is     "Confusing people is my [fort]"   What is the proper way to pronounce this word? When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file $\lim_{n→∞} f(n+x)=0$ results in $ \lim_{x→∞} f(x)=0$ $f\colon [0,\infty) \to \mathbb{R}$ is uniformly continuous.  If $\lim_{n\to \infty}f(n+x)=0$ where $x\in [0,1]$, then $\lim_{x\to\infty} f(x)=0$.  every my trying to solve this is wrong :(  how can i prove this?  and if $f$ is just continuous, what happens to the results My adoptable storage is full. How can I move the data to a bigger MicroSD card? I've got a Moto G 2014 LTE running CM13. When I found out about the whole 'adopt SD card as internal storage' thing, I was quite excited, as the actual internal storage on this phone is tiny. I set up a 16gb micro SD, the biggest I had at the time, and have been using it with minimal problems.  Fast-forward to this day, and I now have a 64gb micro SD that I want to use instead of the 16gb one. However, I'm at a loss as to the best way to copy the data over onto the new one, or if it's even possible. The ideas I've got so far include:   Titanium Backup all [system] apps, factory reset, format new SD and then restore (should work, but a massive pain) NANDroid the SD card onto a USB OTG stick, then restore to the new one (pretty sure this is a bad idea and won't work, but...) Copy all the stuff onto my computer via my phone through a file manager of some sort (I have a linux/linux/windows triple boot, so file format isn't a problem), format the new SD into phone, and copy back (can't be that simple, can it? Hidden/inaccessible files?) Copy the files onto USB OTG with a root file explorer app, reformat the SD as portable, format the new one as adopted, and then copy them back (could work, except for the point below)  with the command adb shell sm set-force-adoptable true, use a root browser to copy all the data over from the old SD, format the old SD as external and remove it, and take the new SD and put it in the SD card slot (seems overly complicated, and also suffers the below pitfall)   The other thing that worries me is mount points: will the apps with externally-stored data know to look at the new SD card for it? Will I have to remount it in a specific location with the shell each boot (or use an init.d script perhaps)? I suppose that it can always be accessed through /sdcard or /storage/emulated/0, but I'm not 100% sure what goes on behind the scenes.  I've got recent NANDroid backups, so if anyone can eliminate the options that definitely won't work (or say which one[s] probably will), I can try them and report back in case someone stumbles across this question in the future.  EDIT: So, my phone further bit the dust and got to the point where it got into a pretty major bootloop. Ended up having to flash a whole new ROM. As such, I probably won't be able to test the full image/decryption/etc. method that I was originally planning. However, I will write up what I've discovered so far in case anyone wants to take up this particular method in the future:   Image the old SD with dd as follows: sudo dd if=/dev/mmcblk0 of=~/SDCardBackup.img, where /dev/mmcblk0 is the location of the sd card as obtainable through lsblk Restore the image you just made to the NEW sd card : sudo dd bs=4M if=~/SDCardBackup.img of=/dev/mmcblk0 (you may have to unmount it first) From here on in, I was following  (thanks @beeshyams!) tutorial, which explains the next steps way better than I ever could have done. The plan was to decrypt the storage and resize the main partition with gparted. I had no idea whether it would work or not, but I felt it was worth a try. However, when I came to run the actual decryption command using the key I'd extracted, I got an error (which I believe was my shoddy linux skills more than anything).   As I say, I have no idea if the above method would work or not even if everything did go to plan. Also, feel free to correct any of my commands above if I mis-typed them (I'm on Windows currently, so this is all from memory.) If this info helps anyone, then good. But until then,  should work fine.  Thanks, Jackdafish so there are some idiosyncrasies with the method they use to invert that part of the image which I can't figure out. It could be that they just invert the luminosity but I don't know how i would do that in a dynamic way. Proving by induction that $\sum\limits_{k=2}^n \frac1{k^2}\le 1$ Is my model any good, based on the diagnostic metric ($R^2$/ AUC/ accuracy/ RMSE etc.) value? If a graph with $n$ vertices and $n$ edges there must a cycle? If 20 independent Bernoulli trials are carried out each with a different probability of success and therefore failure. What is the probability that exactly n of the 20 trials was successful?  Is there a better way of calculating these probabilities rather than simply summing together the combinations of success and failure probabilities? How do I determine if my integrated Intel graphics support "Shader Model 3"? I am trying to play a Steam game on Ubuntu.  The game requires "Graphics: Shader model 3".  How do I determine if my integrated Intel graphics support Shader Model 3?  At present, when I launch the game, I hear the audio, but the screen is entirely black.  Running glxinfo | grep OpenGL yields:  OpenGL vendor string: Intel Open Source Technology Center OpenGL renderer string: Mesa DRI Intel(R) Haswell Mobile  OpenGL core profile version string: 4.5 (Core Profile) Mesa 18.2.2 OpenGL core profile shading language version string: 4.50 OpenGL core profile context flags: (none) OpenGL core profile profile mask: core profile OpenGL core profile extensions: OpenGL version string: 3.0 Mesa 18.2.2 OpenGL shading language version string: 1.30 OpenGL context flags: (none) OpenGL extensions: OpenGL ES profile version string: OpenGL ES 3.1 Mesa 18.2.2 OpenGL ES profile shading language version string: OpenGL ES GLSL ES 3.10 OpenGL ES profile extensions:   I am not sure which (if any) of the above lines answer my question. How to merge multiple Internet connections into one? My PC has a total of 4 NICs, 2 wired Gigabit Ethernet network cards and also 2 wireless network cards. (One Broadcom with proprietary drivers and Ralink with open source software, which works much better than Broadcom.)  My cellphone can share its connection wirelessly to my PC, but I also have a wired Internet connection. So I have multiple Internet connections to access the Internet. How can I merge 2 or more connections together and balance them to enjoy one unified Internet experience that it is the sum of all Internet connections connected to it.  For example if I have a modem with an Internet connection of 1024kB/s and another one that offers 512kB/s and one small one that offers 128kB/s, after load balancing and merging all connections (Bonding or Teaming), I could download at a speed of 1664kB/s using all 3 Internet connections as one for example.  This question has always intrigued me. Syntax highlighting with less, trouble with lexer I have installed python-pygments and using it for syntax highlighting with less as described by mankoff  I put a function in my .bashrc  cless () {     pygmentize -f terminal "$1" | less -R }   it is enabling syntax highlighting with less. But when I am going to open a file like /etc/fstab or /etc/apt/apt.conf a error saying  Error: no lexer for filename '/etc/apt/apt.conf' found   I found option to show pygmentize the lexer with -l at this . But what will be the appropriate lexer for such files? and how to use it?