Connecting to internet over wifi or tether, DHCP does not set DNS
NetworkManager not populating resolv.conf
A Hilbert space is, by definition, a complete inner product space. If $(V,|.|)$ is finite dimensional inner product space of dimension $n$ then it is (topologically) isomorphic to $\mathbb{R}^n$ which is of course complete. My instinct here is to say "and therefore, $V$ is also a Hilbert space". I'm not sure about this step however since completeness depends on the norm and the norm depends on the selected inner product (assuming the induced norm $||x|| = (x | x)^{1/2}$ is used). So, must we place some condition on the inner product or is the topological isomorphism between $\mathbb{R}^n$ enough to guarantee that V is Hilbert? Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball What is the Orthogonal Projection onto the $ {\ell}_{\infty} $ Unit Ball?  Namely, given $ x \in {\mathbb{R}}^{n} $ what would be:  $$ {\mathcal{P}}_{ { \left\| \cdot \right\| }_{\infty} \leq 1 } \left( x \right) = \arg \min_{{ \left\| y \right\| }_{\infty} \leq 1} \left\{ {\left\| y - x \right\|}_{2}^{2} \right\} $$  I managed to get an answer using the . Yet I would be happy to see if someone can derive the answer directly.  Thank You. Primary key or Unique index? At work we have a big database with unique indexes instead of primary keys and all works fine.  I'm designing new database for a new project and I have a dilemma:  In DB theory, primary key is fundamental element, that's OK, but in REAL projects what are advantages and disadvantages of both?  What do you use in projects?  EDIT: ...and what about primary keys and replication on MS SQL server? Explaining Horizontal Shifting and Scaling I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect.  For example, $f(x+1)$ is a horizontal shift to the left (a shift toward the negative side of the $x$-axis), whereas a cursory glance would cause one to suspect that adding a positive amount should shift in the positive direction. Similarly, $f(2x)$ causes the graph to shrink horizontally, not expand.  I generally explain this by saying $x$ is getting a "head start". For example, suppose $f(x)$ has a root at $x = 5$. The graph of $f(x+1)$ is getting a unit for free, and so we only need $x = 4$ to get the same output before as before (i.e. a root). Thus, the root that used to be at $x=5$ is now at $x=4$, which is a shift to the left.  My explanation seems to help some students and mystify others. I was hoping someone else in the community had an enlightening way to explain these phenomena. Again, I emphasize that the purpose is to strengthen the student's intuition; a rigorous algebraic approach is not what I'm looking for. Prove that any conjugate of $a$ has the same order as $a$. I am trying to prove that any conjugate of $a$ has the same order as $a$.  Let $G$ be a group and let $a \in G$.  An element $b \in G$ is called a conjugate of $a$ if $b=xax^{-1}$.  My professor gave us a hint.  Prove $a^k=e$ iff $b^k=e$ for all $k \in \mathbb{Z}$ implies $o(a) = o(b)$.  My first move is to $b^k = (xax^{-1})^k = (x^{-1})^ka^kx^k = (x^{-1})^kex^k = (x^{-1})^kx^k=x^{-k+k}=x^0$  I am not sure that I am doing this correctly?  I am trying to get $b^k=e$.  However when I raise $(xax^{-1})^k$, I am not sure if I what I have done is correct?  I am kind of confused here. Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither? I'm currently considering the ideal $(2,X+1)\subset\Bbb{Z}[X]$. I'm trying to figure out if this is a prime ideal, a maximal ideal, or neither. So far I have attempted to look at the quotient ring $\Bbb{Z}[X]/(2,X+1)$. I know that if this quotient ring is a field, then our ideal is maximal, since $\Bbb{Z}[X]$ is commutative. However I'm stuck on how I should be viewing this quotient ring. How do I allow HTTPS for Apache on localhost? How to implement dual-classing in a non-levelled RPG game? I'm working on an alternate ruleset for a tabletop pen-and-paper RPG (like D&amp;D). Recently I've been toying the idea of abolishing a level system. However, I don't want to remove the ability for a player to multi-class. Are there any games which don't have a levelling system, yet allow multi-classing? How do they do it successfully? How do you detect a network disconnection when downloading a file in java? Suppose that there is a trigonometric equation of the form $a\sin x + b\cos x = c$, where $a,b,c$ are real and $0 &lt; x &lt; 2\pi$. An example equation would go the following: $\sqrt{3}\sin x + \cos x = 2$ where $0&lt;x&lt;2\pi$.  How do you solve this equation without using the method that moves $b\cos x$ to the right side and squaring left and right sides of the equation?  And how does solving $\sqrt{3}\sin x + \cos x = 2$ equal to solving $\sin (x+ \frac{\pi}{6}) = 1$ How to create the matrix attached that has 2x2 blocks in its diagonal and a square outlining them? A question from Kunen's book: chapter VII (H9), about diamond principle DKIM sign outgoing mail from any domain (with Postfix and Ubuntu) I got DKIM setup on my mail server (postfix and ubuntu) so it signs outgoing emails.  I used these instructions:   However, I need it to sign emails from any domain (in the From address) and not just my own.  I'm building an email newsletter service and clients will be sending their own email through the server.  First I set "Domain *" in /etc/dkim-filter.conf.  This got it to include the DKIM headers in all outgoing emails, no matter what the domain.  However, the verification check fails on gmail because it is checking the domain in the from address, and not my domain (and dns record).  Does anyone know how to do this? A homework question from my algebra class asks:     Show that in a local ring $R$ with maximal ideal $M$, every element outside $M$ is a unit.   My argument is that since $M$ is maximal $R /M $ is a field and so for any $ x \in R \backslash M $, $ x + M $ has a multiplicative inverse, which implies $ x $ is a unit.  I don't see where we need the fact that $R$ is a local ring. What does high credit utilization really mean? Detecting constexpr with SFINAE Linux Command Not Functioning As Alias Running out of cards in Exploding Kittens In the Exploding Kittens game, the rules say     You won't ever run out of cards in the Draw Pile, so there is never any need for a reshuffle.   In every game I've played all the cards end up on the discard pile fairly quickly and there is nothing left in the draw pile, so we have to reuse them.  Is this meant to happen? Are we doing something wrong? I will quote a question from my textbook, to prevent misinterpretation:     Let $G$ be a finite abelian group and let $m$ be the least common multiple of the orders of its elements. Prove that $G$ contains an element of order $m$.   I figured that, if $|G|=n$, then I should interpret the part with the least common multiple as $lcm(|x_1|,\dots,|x_n|)=m$, where $x_i\in G$ for $0\leq i\leq n$, thus, for all such $x_i$, $\exists a_i\in\mathbb{N}$ such that $m=|x_i|a_i$. I guess I should use the fact that $|x_i|$ divides $|G|$, so $\exists k\in \mathbb{N}$ such that $|G|=k|x_i|$ for all $x_i\in G$. I'm not really sure how to go from here, in particular how I should use the fact that $G$ is abelian. Transaction log reported full but is not