Ever been asked to send money to this man?
US doctor working in Tripoli wants me to open online account
How can I prove that $2017 \mid 1^{2017}+2^{2017}+\dots+2017^{2017}$? I tried proving it with the use of modulo, however it was to no avail. Afterwards, I  tried researching, for possible theorems, that may help, but that bore no fruit, either. Can you guys please help me proving it, as I am stuck? Thanking you in advance. Proving that the Intersection of any Collection of Compact Sets is Compact I was trying to do this problem this way:  Let $\mathcal{B}=\{B_i\}$ be a collection of compact sets. By Heine-Borel, each of the $B_i$'s are closed and bounded. We already know that the intersection of a collection of closed sets is once again closed, so $\cap \mathcal{B}$ is closed.  If I can prove $\cap\mathcal{B}$ is bounded as well, I can use Heine-Borel to say it is compact. So I was not sure how to show it was bounded, but a friend showed me his way of doing it. He did it the following way:  Let $b,a\in\mathbb{R}$ be an upper and lower bound for $B_1$, respectively. Since $\cap\mathcal{B}\subset B_1, a$ is a lower bound for $\cap \mathcal{B}$ and $b$ is an upper bound for $\cap\mathcal{B}$. Therefore, $\cap\mathcal{B}$ is bounded and then by Heine-Borel, it is compact.  My question is on the paragraph right above. I don't understand why what he did means that $a$ and $b$ are lower and upper bounds for $\cap\mathcal{B}.$ Can anyone explain why this is? Thanks. I have an intuitive scenario. Consider we have a spaceship just below the event horizon of a BH, which is merging with another black hole.  Finally, the singularities merge and we have a single black hole again.  But, in the transient stage, it is unclear to me if a timelike world-line would exist to leave the system.  I suspect, the metric is probably far too complex for an analytical solution, but in the worst case, it could be maybe solved numerically.  As far I know, black hole merges are examined mainly in an inspiral scenario. I suspect, maybe the escape is possible only if they have a hyperbolic-like orbit (i.e. there is no inspiral, but they simply collide).  Is it possible? Factorial of 0 - a convenience? How to clear bash history completely? How to prove that limit doesn't exist using epsilon-delta definition? It is easy to prove the limit exists, all we have to show is there exists a relationship between $\delta$ and $\epsilon$. But how are we supposed to prove limit doesn't exists? The problem is when we are proving for a limit we already know what the limit is and with that, algebra is all that's needed.   Please show through an example (you may show that $\lim_{x\rightarrow0} \frac{1}{x}$ doesn't exist)  If possible please use the explanation scheme that is used by this answer Gendry was born in the Crownlands and should therefore be referred to as Gendry Waters. However, he refers to himself as Gendry Rivers.   Did showrunners forget or is Gendry ignorant of the customs? How do I resize an encrypted LVM to install another copy of Ubuntu? I have an old PowerBook which has been happily running Ubuntu Server for a few months. Now I want to repartition the hard drive and install Ubuntu Client, while keeping my existing installation intact.  When I first installed Ubuntu, I chose to erase the entire hard drive and use it as an encrypted LVM. Now, the installer seems to recognize the partitions on the drive, but it never prompts me for the password to the LVM.  How do I make room for another installation alongside my current one? Getting nauseated from air travel, but it's not motion sickness... what to do? Open subsets in a manifold as submanifold of the same dimension? An open set in an $n$-manifold is clearly a submanifold of the same dimension as its containing manifold (see open manifolds).   Now, given an $n$-manifold $M$, is it true that a set, to be the underlying set of a submanifold of $M$ with dimension $n$, must be open? Can a wealthy investor invest in or make a deal with a company before it goes public / IPO? Can a wealthy investor invest his money in any company before it goes public / IPO? I am referring to a recent Goldman Sachs and Facebook deal worth $450 Million at a valuation of $50 Billion dollars.   I want to know what is the procedure and how are these valuations made prior to the company going public? Is is possible that an investor could raise capital from investment banks, private equity, or commercial banks to re-invest in a pre-IPO deal at some valuation?  Knowing that angel investors don't provide so much money, can they play their role here with a normal investor? Mirror Modifier making ugly smoothing on mirrored faces The model is vivisected right down the middle along the z axis. The right leg is rendering funny and I assume if I can get that fixed everything else will fall into place. I tried flipping normals, changing shading types - can't think of anything else to do. Email SMTP validator I need to send hundreds of newsletters, but would like to check first if email exists on server. It's called  validation, at least I think so, based on my research on Internet.    There's several libraries that can do that, and also a page with open-source code in  (), but I have hard time reading ASP Classic, and it seems that it uses some third-party library...    Is there some code for SMTP validation in C#, and/or general explanation of how it works? Why is the well ordering principle counter-intuitive? I read  that while 'The Axiom of Choice agrees with the intuition of most mathematicians; the Well Ordering Principle is contrary to the intuition of most mathematicians'. I don't understand why this is so. According to Wikipedia, 'the well-ordering principle states that every non-empty set of positive integers contains a least element'. This is quite a straightforward definition. Is it the way you derive the equivalence of the Axiom of Choice and well ordering principle that makes it counter-intuitive or the definition of the least element? Store won't open after upgrade MySQL Conditional Insert In D&amp;D 5, the saving throws for spells has the following formula:  The DC is set to 8 + prof bonus + magical stat bonus.  The target then makes a saving throw, adding their stat bonus and hoping to get above that DC.  Instead of having the defender roll the saving throw, we would like the attacker to roll the attack against the "defense" of the monster. (Mainly to make play by post run smoother)  Would this mean that the attacker just rolls d20+prof + magic stat bonus, and they try to get a number which is higher than 8+ monster def stat bonus, or is there a different formula which better maintains the math? (This math sounds wrong to me, so I assume there is a better formula) What Did Lyanna Stark Say to Ned Stark? In the final episode of season 6 we see that Lyanna Stark is whispering something to Ned. What is she saying? Viewing all my questions from Android app Let $F$ be a field and $x\in F$. If $x=-x$ and $1\neq -1$, then $$0=\frac{x+x}{1+1}=\frac{1+1}{1+1}x=x.$$ This means that the statement in the title is true if and only if $1\neq -1$. But how do we know that $1\neq -1$ for an arbitary field?