Earth man sent by superior to distant empire, dueling, caste by height and strength, honorary military post
Spy from Earth studies Galactic Empire nobility and prevents plot to depose Emperor
How to respond to "How much funding will you bring?" as an interview question for a faculty job? Prove that given $A\subseteq\mathbb{R}$, if has a maximum $a_0$, then $a_0$ must be the supremum.   In order to prove this, I have written the following:  Let $A\subseteq \mathbb{R}$, nonempty set because $a_{0}$ $\in A$ for hypotesis. Then, since $a_{0}$ $\in A$ is the largest element of the set $A$   (i.e. for each element $A$ of A we have that $ a\leq a_{0}$) $A$ is bounded above. Then, A has a supremum. Let $s$ be the least upper bound of $A,$ so we have that for each element $a$ of $A$, $a\leq s$, for being $s$ an upper bound. In particular, $a_0\leq s$, which implies that $s=a_0$.   Then, we have that $\sup(A)=\max(A)=a_0$, which is exactly what we wanted to prove.  Observation: this proof is true if $s \in A$   I'm not sure if my proof is correct. I will be thankful if someone tells me. Java: Prefix/postfix of increment/decrement operators? Why are light rays able to cross each other? See the image first:   Why are light rays able to cross each other? Air isn't able to. I'm reading through a proof in my lecture notes:     Every convergent sequence of a metric space has a unique limit.   Suppose $\lim_{n \to \infty} x_n = l$ and $\lim_{n \to \infty} x_n = m.$ Then for every $\epsilon &gt; 0,$ there exists $N$ such that for every $n \geqslant N,$  $$d(l,m) \leqslant d(l,x_n) + d(x_n,m) &lt; \epsilon + \epsilon = 2 \epsilon. $$  So $(\star) \hspace{1mm} 0 \leqslant \frac{d(l,m)}{2} &lt; \epsilon \Longrightarrow \hspace{1mm} (\star^\prime) \hspace{1mm} \frac{d(l,m)}{2} =0 \Longrightarrow l = m.$  I can follow the proof up until the jump from $(\star)$ to $(\star^\prime)$. Why does $\frac{d(l,m)}{2}=0$? Of Half-elven and mortal life Let $$f(x)=\begin{cases} \sin \tfrac 1 x &amp;\text{if $x\ne 0$}\\ 0 &amp; \text{if $x = 0$.}\end{cases}$$ I have to show that $f$ has the intermediate value property. That is, for any $a &lt; b$, if $y$ is any real number such that $f(a) &lt; y&lt; f(b)$ or $f(a)&gt;y&gt; f(b)$, then there exists a $c \in (a,b)$ such that $f(c)=y$.  I feel like I kind of know how to go about completing this. I just am curious as to if I have to create a bound such as letting $a = -1$ and $b = 1$, or keep $a$ and $b$ both arbitrary. Pulling a CSV file from website into QGIS with ability to automatically refresh? Why is removing instationarities a good thing when trying to forecast a time series? JavaScript + Unicode regexes I think it would be very useful.  I have a question that I have an open bounty on. Putting up said bounty brought my reputation below the point where I am allowed to comment on other peoples' posts. It's so frustrating not to be able to comment and give feedback on the answers given!  Especially since it would be helpful, for them, me, and the readers, to know particularly what is good and isn't good about their answer, and therefore give some better guidelines to future answerers on how they can win the bounty. How to get my 4yo daughter's fixation on my belly button under control? I don't know where to begin with this question. It's awkward and to be honest, it makes me feel rather uncomfortable. Simply put, I'm led to believe that my four year old daughter is obsessed with my belly button. It all started one day during the summer when she was three. I decided to take my family to the pool, and I guess I didn't see my daughter follow me into the changing room. Mind you, she's still at the age where it's appropriate to see her parents naked, so I wasn't surprised when, after I finished changing into my bikini, I turned around to see her staring at me.  I followed her gaze and saw her looking directly at my belly button. I asked her what she was looking at and she screamed "mommy, I can see your belly button!" which made me giggle. I picked her up and kissed her forehead, telling her that everyone has a belly button.  I think I might have accidentally given her a green light, because over the next year she constantly asks me if she can stick her finger in my belly button, and if I don't let her, she begins to scream.  For her fourth birthday, she requested that I wear nothing but a sports bra and underwear (in toddler speak. It sounded like "mommy, show your belly button for my birthday!" I could have simply worn a crop top but i didn't want to risk her throwing a temper tantrum)  My husband obviously doesn't mind, because he gets to look at my belly button all the time but it really upsets me that my daughter's finger is constantly in my belly button.  Tomorrow is her fifth birthday and I want to discuss with her that it's not appropriate to always be poking my belly button. Any ideas on how i can talk to her without her throwing a screaming fit? Mark's generosity in this crisis seems to more than make up for his earlier stinginess.   Should those sentences always be avoided, or are there cases where they are valid? What techniques have been used to repeat geometry or other detail to the infinite horizon? Calculating Latitude/Longitude X miles from point? I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. Fast, accurate 2d collision I'm working on a 2d topdown shooter, and now need to go beyond my basic rectangle bounding box collision system.  I have large levels with many different sprites, all of which are different shapes and sizes. The textures for the sprites are all square png files with transparent backgrounds, so I also need a way to only have a collision when the player walks into the coloured part of the texture, and not the transparent background.  I plan to handle collision as follows:   Check if any sprites are in range of the player Do a rect bounding box collision test Do an accurate collision (Where I need help)   I don't mind advanced techniques, as I want to get this right with all my requirements in mind, but I'm not sure how to approach this. What techniques or even libraries to try. I know that I will probably need to create and store some kind of shape that accurately represents each sprite minus the transparent background.  I've read that per pixel is slow, so given my large levels and number of objects I  don't think that would be suitable. I've also looked at Box2d, but haven't been able to find much documentation, or any examples of how to get it up and running with SFML. Which SUSY models are affected by the recent LHCb result? Connecting MySql with Android without using PHP Syncing folders outside Dropbox using Symbolic Links and Junctions I've been reading a lot of information on this and yet I'm still unsure if its possible.  What I want to achieve is: sync a folder that is outside Dropbox and any changed to that folder or the files within get mirrored to the Dropbox folder and the Dropbox server.  This is what I've tried: I've install Link Shell Extension. Picked a folder with 10 pictures inside and created a junction for it inside the Dropbox folder. When I delete a pictures from inside the original folder (outside Dropbox) the change is reflected in the Junction folder inside Dropbox Folder, not on the server.  The exact same behaviour with the Symbolic Link option.  If I manually select Pause Syncing from Dropbox system tray icon and then Resume syncing = it uploads the changes to the server.  I know I can move all my files inside Dropbox folder and create the junctions/symlinks at their original locations but I want to do it the other way around.  Also what is the difference between choosing the Junction and Symbolic Link Option in regards to a folder?  Thank you. Show that every monotonic increasing and bounded sequence is Cauchy.