I'm going to build a city and I need to know where the center is. I'm using version 0.6.1. How can I figure out where the exact center is located?
I'm currently building a town in Minecraft Pocket Edition and I'm wondering how many blocks long and how many blocks wide the world is.
What's the deepest reason why QCD bound states have integer charge? I am calculating the class group of $\mathbb Q(\sqrt 6)$. My working is as follows:  The Minkowski bound is $\lambda(6)=\sqrt 6&lt;3$ so we only need to look at prime ideals of norm $2$. $2$ divides the discriminant, $24$, of $\mathbb Q(\sqrt 6)$, so $2$ ramifies, and so for any prime ideal $\mathfrak p$ of norm $2$, $\mathfrak p^2$ is principal. But $(2, \sqrt 6)^2=(2)$, so $\mathfrak p=(2, \sqrt 6)$ has norm $2$. If I can show $\mathfrak p$ is not principal, then I can conclude that $Cl(\mathbb Q(\sqrt 6))\cong C_2.$ But if there was an element of $\mathcal O_{\mathbb Q(\sqrt 6)}$ of norm 2, this would correspond to a solution of the diophantine equation $x^2-6y^2=2$. Clearly $x$ is even, so writing $x=2n$ we get $2n^2-3y^2=1$. Now reducing modulo $3$, we get $2n^2\equiv 1 \pmod 3$ which has no soultions. Hence $\mathfrak p$ is not principal and $Cl (\mathbb Q(\sqrt 6)) \cong C_2.$  However,  says that the class group is trivial. Where have I gone wrong? What am I misunderstanding? Is $(2, \sqrt 6)$ principal? Word for person who looks for flattery Is the cube root of a prime number rational? The question is: if $P$ is prime, is $P^{1/3}$ rational?   I have been able to prove that if $P$ is prime then the square root of $P$ isn't rational (by contradiction) how would I go about the cube root? Would time speed up near a large body of negative mass relative to observers in micro gravity? Time tends to slow down near objects with large amounts of positive mass relative to observers in micro gravity.  Considering that negative mass is the opposite of normal mass and would time tend to speed up near a body of negative mass relative to observers in micro gravity? How can a CPU deliver more than one instruction per cycle? diagram software for Ubuntu? Is there a LaTeX/TeX preprocessor/inliner that replaces only selected macros with their definitions? I am reading Velleman's "How to Prove it", and in one example he proves  $\neg \exists x P(x)  \implies \forall x \neg P(x)$    in the following way:    Suppose $\neg \exists x P(x)$. Let x be arbitrary. Suppose $P(x)$. Since we have a specific $x$ for which P(x) is true, it follows that $\exists x P(x)$, which is a contradiction. Therefore $\neg P(x)$. Since $x$ was arbitrary, we can conclude that $\forall x \neg P(x)$, so $\neg \exists x P(x)  \implies \forall x \neg P(x)$    What makes me confused is the line in bold text, that is "Suppose $P(x)$". The reason is that he writes that he is doing proof by contradiction, but $P(x) \not\iff \neg\forall x \neg P(x)$. He is not treating all possible cases where $\forall x \neg P(x)$ is false by assuming $P(x)$, does he? So how can this be a valid proof by contradiction?    Edit: I deleted my first example since it was clearly not representative for the problem.  Edit 2: So the thing that I am opposing I guess is that $\neg \forall x \neg P(x)$ is not $P(x)$. And from what I have undestood, a proof by contradiction should use the negation of the consequent which I do not think that Velleman does. Question: If $G$ is a finite group such that the product of its elements (each chosen only once) is always $1$, independent of the ordering in the product, what can we say about $G$?  I was trying to conclude that $G$ must be abelian (I am not sure about this). I proceed as follows: if $|G|\leq 4$, then obviously, $G$ is abelian. Suppose $|G|&gt;4$. Then consider products of all elements in the order $a^{-1}b^{-1}ab cc^{-1}dd^{-1}....$. This, being identity, implies that $a^{-1}b^{-1}ab=1$, i.e. $G$ is abelian.  BUT, the problem is in $a^{-1}b^{-1}ab$, the elements $a$ and $a^{-1}$ should be distinct, and similarly for $b$. Otherwise, the product $a^{-1}b^{-1}ab cc^{-1}dd^{-1}....$ is not in the prescribed form as in question.  Also, note that the cyclic group of order $4$ doesn't satisfy that $abcd=1$ where $\{a,b,c,d\}\cong \mathbb{Z}_4$. How to design partitions for SSHD? Remove Meta Privilege for MSE (only) What I am asking here is to please remove the privilege to participate in Meta for MSE.  This privilege is literally useless. You can't really have a meta site for a meta site. There's no Meta.Meta.SE here or any other SE site out there: Meta.SE covers for every site in SE, including itself.     When users find out that you don't really get anything new, it's kinda sad for those people. There is no use for it except just to be there and fill up the space between the first and third privilege. Privileges should be shown only if you earn something new, and this privilege to participate in the meta isn't new because it's where you report problems in all of SE, including Meta.SE.    So please remove the privilege to participate in meta just for Meta.SE.    This is not a dupe as this is a feature-request to remove it, not support on why it is there. Seems that I just proved $2=4$. Solving $x^{x^{x^{.^{.^.}}}}=2\Rightarrow x^2=2\Rightarrow x=\sqrt 2$.  Solving $x^{x^{x^{.^{.^.}}}}=4\Rightarrow x^4=4\Rightarrow x=\sqrt 2$.  Therefore, $\sqrt 2^{\sqrt 2^{\sqrt 2^{.^{.^.}}}}=2$ and $\sqrt 2^{\sqrt 2^{\sqrt 2^{.^{.^.}}}}=4\Rightarrow\bf{2=4}$.  What's happening!? When a Battle Master fighter gets a critical hit and uses a maneuver that adds a superiority die to the damage, is that damage die doubled? The Battle Master fighter has access to a number of maneuvers that add a superiority die to the damage roll. For instance, the Trip Attack maneuver says (PHB, p. 74):     When you hit a creature with a weapon attack, you can expend one   superiority die to attempt to knock the target down. You add the   superiority die to the attack’s damage roll, and if the target is   Large or smaller, it must make a Strength saving throw. On a failed   save, you knock the target prone.   The Critical Hits rule states (PHB, p. 196):     When you score a critical hit, you get to roll extra dice for the   attack’s damage against the target. Roll all of the attack’s damage   dice twice and add them together. Then add any relevant modifiers as   normal. [...] If the attack involves other damage dice, such as from   the rogue’s Sneak Attack feature, you roll those dice twice as well.   During our game, the fighter PC rolled a critical hit. He then wanted to use a superiority die to use the Trip Attack maneuver to trip the enemy. Based on the above rules, is the damage from the superiority die also doubled?  I'm assuming the answer is yes based on the last statement in the Critical Hits section, but I wanted to confirm. Number or regions formed when $n$ points on a circle are joined The maximum number $R_{n}$ of regions formed when $n$ points on a circle are joined in pairs is $\frac{1}{24}\left(n^{4}-6n^{3}+23n^{2}-18n+24\right)$.  This is a fact that I have read in several essays on the dangers of jumping to conclusions in mathematics.  In your opinion, what's the quickest (and/or nicest) way to prove this formula?  Professor  explains somewhere an especially convincing way to tackle this pearl following an idea which a certain high schooler in one of his talks (lectures?) came up with; yet, I don't remember  where it was that I actually read this...  Let me thank you in advance for your insightful replies. Why bar magnet can produce magnetic field? Understanding downside of triple-leveraged ETF What happens to the price of the triple-leveraged ETF if the S&amp;P 500 loses more than one-third of its value (i.e., the return is below -33 1/3%)?  Does it mean the value is equal to zero? Monitoring contents of files/directories? Getting a random object from NSArray without duplication How to include PHP files that require an absolute path? I have a directory structure like the following;     script.php      inc/include1.php   inc/include2.php      objects/object1.php   objects/object2.php      soap/soap.php   Now, I use those objects in both script.php and /soap/soap.php, I could move them, but I want the directory structure like that for a specific reason. When executing script.php the include path is inc/include.php and when executing /soap/soap.php it's ../inc, absolute paths work, /mnt/webdev/[project name]/inc/include1.php... But it's an ugly solution if I ever want to move the directory to a different location.  So is there a way to use relative paths, or a way to programmatically generate the "/mnt/webdev/[project name]/"?