Proof in Intuitionistic logic: $\neg \neg A \to \neg \neg B \vdash \neg \neg (A \to B)$
Does double negation distribute over implication intuitionistically?
Showing OSM source acknowledgment on the map in QGIS? I am using OpenStreetMap as a base layer via XYZ tiles in QGIS 3.01.  I can't seem to find a way of having source acknowledgement appear on the lower right corner of the map.  Can somebody point me in the right direction? $\Delta U$, $C_p$, $C_v$ for an ideal gas process Which external Javascript libraries work with Lightning Locker Service? Components often seem to work with external libraries until the Locker Service is enabled. What libraries work with locker service enabled and where can I go to find out? A Basic Question about Gravity, Inertia or Momentum or something along those lines Why is it that if I'm sitting on a seat on a bus or train and its moving quite fast, I am able to throw something in the air and easily catch it? Why is it that I haven't moved 'past' the thing during the time its travelling up and down? I have this weird object (vascular tree) which is empty inside, but closed from the top and the bottom:  However, it is empty inside, which makes me unable to use boolean on a bigger object (I want to make a hole in an object through which this object will go through). So I thought I should fill it and then try to boolean. But, how do I fill it?  Thank you sincerely. I need to make Windows 7 STOP disabling the wifi adapter when the wired LAN is connected I have added the png transparent image with the setting and its not showing transparent black background is seen. I have the base color aluminum and i want to add that logo of png on to it. The image is black letter with transparent background why its showing in white letters and black background. May i know where im going wrong any suggestion or help. Programmatically get own phone number in iOS Is there any way to get own phone number by standard APIs from iPhone SDK? To give some background, I am attempting to solve the problem from Artin's algebra textbook which was already asked in this link:  Now, I would like to prove the following two claims which are not obvious to me. If I can prove these, I will be able to show that $\zeta_5\notin \mathbb{Q(\zeta_7)}$ as needed. I suspect that both claims will have similar proofs.  Claim 1: $\zeta_5$ has degree $4$ over $\mathbb{Q}$ Claim 2: $\zeta_7$ has degree $6$ over $\mathbb{Q}$  Attempt to prove Claim 1 Let $α=\zeta_5$. I would like to find the monic irreducible polynomial for $α$, but unfortunately I do not know what it is yet. I see $α=cos(\frac {2π}5)+isin(\frac {2π}5)$ and $α^4=cos(\frac {4π}5)+isin(\frac {4π}5)$. Please help me to find the irreducible polynomial, and (ideally) to show that it is irreducible. What is the difference between a 'closure' and a 'lambda'? Is It Possible to NSLog C Structs (Like CGRect or CGPoint)? I want to be able to debug C structures without having to explicitly type every property that they consist of.  i.e. I want to be able to do something like this:  CGPoint cgPoint = CGPointMake(0,0); NSLog(@"%@",cgPoint);   Obviously the '%@' won't work, hence the question. Internal or external oscillator I always use the internal oscillator that pics have as I have never found the need to run anything at higher frequency than 8 MHz (which is the fastest the pics I use tend to be able to go). Are there any reasons, beyond going above 8 MHz, that mean I should use an external oscillator? It just seems like one more thing to go wrong to me but I'd be interested to hear what others do. How do I find (or exclude) all directories and sub-directories matching a certain pattern (in Linux)? Your answer is in another castle: when is an answer not an answer? Would someone give a thorough explanation of 1.14 Minecraft's /data modify? Okay, so I've been searching all over the internet for an explanation of data modify ever since I heard Sethbling passively mention it in one of his videos. The only  thing I could find on it was the wiki and the update log for the 1.14 snapshot. So, I checked these, and they hardly explained it at all. I can get /data modify block 123 20 123... and that's as far as I get.  Minecraft wiki does not at all define clearly what  is (the thing meant to go after coords), nor does it specify what each operation does to what. Operations include (without explanation, and excluding set (which it does explain)): append, insert, merge, and prepend. Then, it has from|value as the next option, which aren't explained either. After this, it just has block/entity and coords/id. So, I know the format (mostly), but I haven't the slightest idea what any of it means. And nothing I've seen on the internet even mentions the command save for Minecraft wiki itself.  Please explain if you know what data modify is. Thanks! The energy of a moving object is $E = mv^2\;.$ That is it increases with velocity squared.  I walk at say 3 miles per hour, or lets round that down to 1 meter per second for a slow walk. I weigh less than $100~\mathrm{kg}\;,$ but lets just round that up to $100~\mathrm{ kg}$ for convenience (it is just after Christmas).  So when I walk along the pavement, I have $100~\mathrm{kg\; m^2 s^{-2}}$, 100 joules of kinetic energy.  Now I get on a passenger jet, which is cruising at around 500 knots, call that 250 meters per second.  In my seat I have $100\times 250^2 = 6250000$ joules of kinetic energy. But when I walk down the aisle I have $100\times 251^2 = 6300100$ joules of kinetic energy. The difference between these is: 50100 joules.  It feels the same to me, walking down the pavement as walking down the aisle of the plane. I didn't have to make some huge effort to get up to speed on the plane, yet I needed 500 times the energy to do it.  How is this possible, and where did the energy come from? Diagonalisation and characteristic polynomial Let $A\in M_3(\Bbb R)$ which is not a diagonal matrix. Let $P$ be a polynomial (in one variable), with real coefficients and of degree 3 such that $P(A) = 0$. Pick out the true statements:  a. $P = cP_A$ where $c \in\Bbb R$ and $P_A$ is the characteristic polynomial of $A$;  b. if $P$ has a complex root (i.e. a root with non-zero imaginary part), then $P = cP_A$, with $c$ and $P_A$ as above;  c. if $P$ has a complex root, then $A$ is diagonalizable over $\Bbb C$.  I guess b and c are true although I am unable to disprove a. Because A could satisfy $(X-A)$ but this is not a polynomial. Now if $P$ has a complex root, then its conjugate too is its root as the polynomial has  real coefficients. As we all know An odd degree polynomial has always a real root, what we have is three distinct roots. Since $A$ satisfies the polynomial the only difference between the characteristic polynomial and $P$ has to be a constant. Redirect STDERR and STDOUT to different variables without temporary files Forgotten the pattern and phone not showing the "forgot pattern" button. I upgraded my Moto G2 to Android Lollipop using over-the-air upgrade. It was awesome but I set a pattern lock which I forgot. Usually after 5 wrong attempts it shows the "forgot password" button but it is not showing that button even after 100 wrong attempts. How to unlock the phone? Ain't and negatives