I am surprised that I wasn't able to find this question asked before, but I could see it used as quite an epic showing:  The old lady brings your group over to the mountain base filled with sharp cliffs, jagged rocks, and a path no wider than your foot. The roaring waterfall makes the air crisp, clean, and humid as she stops by a sign adorned with a bell and a rope, looping all the way up the mountain. Turning to your group with a kind smile, the guide pulls the rope and stands in wait. &quot;Well, aren't you going to take us to him?&quot; one of the players exclaim, annoyed at this old hag's smugness. Just as soon as the words escaped their mouth the bell rings, causing the granny's wrinkled face to beam with a smile.* &quot;Oh, he's on his way sonny,&quot; She says pointing her knotted cane towards the top of the waterfall. As your party looks, there is a man falling what must be 1000 ft straight into the mouth of the waterfall, finally getting swallowed by the mist below. A second later, the man you have been searching for, the man who jumped down the waterfall, emerges from behind the waterfall, dry and unscathed.  Now though this seems quite epic, the way that the guy defied death was by using a teleporting spell when he was covered in the mist to reappear on the rock behind the waterfall. From what I understand , teleportation spells do not conserve momentum, so his falling speed would go from 20d6 damage to 1ft no damage. Is this truly how powerful teleportation spells can be?
If I fall off a cliff - say, 1000 feet - can I wait (readied action?) until I am near enough to the ground (my understanding is you fall 500 ft/round) then  safely to the ground? Or, does the momentum from the fall carry over through the teleport and I still splatter across the rocks?
Why is the relationship between atomic number and density not linear? How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition) I'm doing exercise on discrete mathematics and I'm stuck with question:     If $f:Y\to Z$ is an invertible function, and $g:X\to Y$ is an invertible function, then the inverse of the composition $(f \circ\ g)$ is given by $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$.   I've no idea how to prove this, please help me by give me some reference or hint to its solution. The question asks to compute:   $$\sum_{k=0}^{n-1}\dfrac{\alpha_k}{2-\alpha_k}$$   where $\alpha_0, \alpha_1, \ldots, \alpha_{n-1}$ are the $n$-th roots of unity.   I started off by simplifiyng and got it as:  $$=-n+2\left(\sum_{k=0}^{n-1} \dfrac{1}{2-\alpha_k}\right)$$  Now I was stuck. I can rationalise the denominator, but we know $\alpha_k$ has both real and complex components, so it can't be simplified by rationalising. What else can be done? Full width image in beamer? I accidentally killed a noble, now every guard wants to kill me. Is there any way I can get rid of the bounty? How do I generate random integers within a specific range in Java? How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum. Why do Borg move so poorly (like 50s movie robots)? Make \cite{my reference} show name and year I am trying to figure out how to make author's name and year show up every time I make a reference.  For example:  my_bibtex.bib has this entry:  @article{Franklin1999,  author = {Franklin Allen and Risto Karjalainen}, title = {Using genetic algorithms to find technical trading rules}, year = {1999}, volume = {51}, pages = {245-271}, journal = {Journal of Financial Economics}  }   If in my_paper.tex I use this line:  Important result has been found by \cite{Franklin1999}   My output looks like:  Important result has been found by [1]   But I want it too look like:  Important result has been found by Franklin 1999   I there a way to do it?  My bibliographystyle is set to plain  \bibliographystyle{plain}  \bibliography{my_bibtex} The default in lyx is to have   I. First part (roman number)   Section 1   1.1 Subsection 1  and I'd like to have   First part (arabic number)   1.1 Section 1  1.1.1 Subsection 1  etc.   Any suggestion? Thanks a lot in advance! Preserve blend mode effect when underneath layers are disabled? (Photoshop) Laptop randomly waking up = Hibernate / Low Battery? What is needed for a game's stats to be saved? Last night I played a few games with my friend. While in the last game, I suddenly remembered something I had to do and was about to leave but my friend told me that I would lose my progress if I did so. I stayed until the end, through the scoreboard screen and quit while the next map was loading. Taking a look  now, I can't see any of yesterday's games. I don't remember how much XP I had yesterday so there is no sure way for me to check that. I had gotten a dozen ribbon and I don't see them in the feed, but there could be specific conditions to be showing them.  My questions then.   If you quit a game early, do you lose progress / XP? What if you quit on the scoreboard? Do you need to wait for the next map to load to save your progress? Any idea why the games aren't showing up? Some of them I definitely waited for the next map to load. Is there a delay for them to be shown on Battlelog?   Thanks. How to break the Y axis in an Excel sheet I want to break the Y-axis in an Excel sheet. How can I do that?  For example, suppose I have the data in a range from 0-7000 and then range from 22000-28000. I want a break in the Y axis from 8000-20000. Centering figure captions in IEEEtran I am working on a paper using the IEEEtran template in LyX.  I have run into a problem: While the contents (in this case, a table) of the figure float are centered, the caption is aligned to the left (see screenshot below). How can I center the caption as well?    This is generated by the following LyX document:    What I've tried:   Center the table (the table is centered) Center all the contents in the float (only the table is centered) Select the caption and center it (no effect)   Technical details:   LyX 2.0.5.1 Mac OS X 10.7.5 (Lion) All centering was performed by Right Click>Paragraph Settings>Align: Center Topic models and word co-occurrence methods The title says it all.  If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?  So my son posed me an interesting question today: since light travels as fast as anything can go, what if I shined light when moving in a car?  How should I answer his question? A friend sent a long a file (a .rar) he wanted me to check out for him before he installed it.  I downloaded it and unrared it with no problems, but it was full of .exe's instead of the intended contents (fonts) so I advised him to delete it immediately and not use.  I then proceeded to do the same, but the folder simply will not delete. Oddly the files went fine, and I never ran anything, but this is what I'm seeing:   Could not find this item  This is no longer located in C:\Users\This_User\Desktop. verify the item's location and try again.   I've tried the following things with no help:   Using "Unlocker" to Unlock and delete Using move on reboot and rebooting Using PendMoves (from sysinternals) and rebooting Elevating a cmd line, doing a dir /x to get the short name of the folder, and then del 'shortna~1' Moving the folder to a new folder and then trying to delete the parent folder   I'm on Windows 7 RTM, very fresh install. Any thoughts?  Update: Just to confirm, I've run Hijack this and half a dozen other malware detectors, and everything came back clean (no extra processes, no other obvious badness). Rebooting in safe mode didn't help either. Let $\mathbb{Z}[X]$ be the ring of polynomials in one variable over $\Bbb Z$.  My question: Is every prime ideal of $\mathbb{Z}[X]$ one of following types? If yes, how would you prove this?  $(0)$.  $(f(X))$, where $f(X)$ is an irreducible polynomial.  $(p)$, where $p$ is a prime number.  $(p, f(X))$, where $p$ is a prime number and $f(X)$ is an irreducible polynomial modulo $p$. How fast does electricity flow? What is the best choice for .NET inter-process communication?