Is it possible for other half-elves (besides Earendil, Elwing and their descendants) to be presented with the choice of immortality? I know that through Earendil's line that exception was granted to him and his family. However, I wonder if it is possible for some of the other half-elves to be presented with that similar option.   Whilst through Imrazor and Mithrellas, their son Galador died as a mortal, nothing is known of Gilimith, their daughter.  Surely there must have been other examples or a slight possibility for other cases.
Of Half-elven and mortal life When half-elvens choose mortal life, how would their bodies behave?  Half-elven are always elves by nature. Ever since they're born, their physical body and behaviour would be elvish - they have keen senses, they don't get physically weary, no illness, and so on.  Half-elvens are then offered a choice - Immortal elvish lives or mortal fate of men. When they choose the latter, like Elros and Arwen did, what would happen to their elvish nature? Would they lose it? I don't think they would lose their pointy ears, but what about the other elvish features that I mentioned before?  Are there any canonical references?
Why and how does C# allow accessing private variables outside the class itself when it's within the same containing class? How can we make First letter Capital while using trigonometric functions. eg: \cos (60^\circ) gives simple cos (all in small). What is needed is 'Cos' (with initial capital). For italics in mactex i used \it but it didn't italicized 'cos' only the number '60'. So how to do that? A clock in freefall Time dilation  using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$  For such a non rotating spherical body, what would the time dilation of a clock in vacuum free-falling from infinity be?  (If the answer is non-trivial; a high level outline of the calculation would suffice / be appreciated)  Edit: I am currently working on an iOS app that is trying to model the mechanism underpinning relativity.  So, far the mechanism that I have created is shockingly simple and shockingly good at conforming to Relativity.  However, I am trying to break it.  I am trying to find any possible areas where the two may diverge.  I have noted that using my model a clock in freefall will experience no time dilation, i.e. $t_0=t_f$ and I want to make sure Relativity agrees.  I have noted the gravitational component of time dilation above.  Since my clock is moving one might also expect a kinematic time dilation.  I can calculate the velocity of my clock: $$E_k=\frac{1}{2}mv^2$$ $$E_p=\frac{-GMm}{r}$$ $$v=\sqrt{\frac{2GM}{r}}$$ Plugging this velocity into the kinematic time dilation equation: $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$ $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{2GM}{rc^2}}}$$  At this point one might make the observation that the kinematic dilation is the inverse of the gravitational dilation and therefore conclude that: $$t_0=t_f$$ How to plot a surface from a set of data? Disclaimer: I already read questions like  and  but these did not solve my problem.  I have this set of data:  x       y       z 2.17    0.001   0.82044815 2.17    0.002   0.82345825 2.17    0.004   0.82679255 2.17    0.008   0.83334715 2.17    0.016   0.84395915 2.17    0.032   0.8584953 2.21    0.001   0.77582165 2.21    0.003   0.78520505 2.21    0.009   0.80205985 2.21    0.027   0.83085105 2.24    0.001   0.7227885 2.24    0.002   0.73391615 2.24    0.005   0.7543979 2.24    0.015   0.78798745 2.24    0.003   0.74176635 2.24    0.009   0.77064805 2.24    0.027   0.81042375 2.26    0.001   0.66545585 2.26    0.003   0.7012046 2.26    0.005   0.721067 2.26    0.009   0.7447984 2.26    0.015   0.76715245 2.26    0.027   0.794177 2.27    0.001   0.62916195 2.27    0.003   0.6774642 2.27    0.009   0.72961785 2.27    0.027   0.7861086 2.28    0.001   0.5750828 2.28    0.003   0.65059675 2.28    0.005   0.6802631 2.28    0.009   0.7145367 2.28    0.015   0.74447695 2.28    0.027   0.7774403 2.29    0.001   0.51357255 2.29    0.002   0.581053 2.29    0.003   0.6173075 2.29    0.009   0.6972096 2.29    0.027   0.76793225 2.31    0.001   0.36997965 2.31    0.002   0.474415 2.31    0.003   0.53649295 2.31    0.009   0.6587164 2.31    0.016   0.70870255 2.31    0.027   0.7482423 2.31    0.05    0.7912395 2.34    0.001   0.2204104 2.34    0.002   0.316308 2.34    0.003   0.39256745 2.34    0.004   0.45240835 2.34    0.009   0.5883453 2.34    0.016   0.6590771 2.34    0.027   0.71444205 2.34    0.05    0.7690014 2.38    0.001   0.13286995 2.38    0.002   0.1828288 2.38    0.004   0.2980268 2.38    0.008   0.4507145 2.38    0.016   0.58417075 2.38    0.032   0.6833616   And if I plot it in Mathematica (with ListPlot3D[data]) it looks, without further tweaking and fiddling around, like:    But if I try this pgfplots code  \begin{tikzpicture}   \begin{axis}     \addplot3 [surf] table {data.txt};   \end{axis} \end{tikzpicture}   I only get this:    What do I have to do to get a surface like in Mathematica (color, smoothness, style, etc. does not matter, just a closed surface)? Refreshing Formula Fields Dynamically (without save) I have an "invoice" custom object which has a couple of summarising formula fields in. I also have a complicated and dynamic visualforce page for building the invoice objects.  As the user is completing this form, different areas are dynamically updated to show "latest" values. This is all fine where I am copying data about or performing bespoke lookups and maths, but - in what is really the simplest case - a formula field, I can find no way to get the value to update, without performing some weird cyclic save + reload of the whole object.  This is inappropriate for a couple of reasons (the object should not be saved until the invoice is complete + accepted) and the other option I have found online is to spoof the value by duplicating my formula field maths into the custom controller and re-executing them there - also unacceptable from a code/logic location/duplication perspective.  Is there anyway to "force" an object/page to recalculate it's formula fields, either through standard or extended controllers? I'm Australian and have obtained my Canadian working visa. However rather than flying direct to Canada I am meeting an American friend in LA and driving across the border. I have a return flight booked back to Australia from LA in March of next year too. Will the esta visa will be enough to enter the USA because I have my Canadian working visa and plan to travel there? Or will there be a problem because my return flight is booked later then the 90 days allowed on the visa. The nautilus-open-terminal package adds a menu/right-click option to open a terminal in the current directory.  I want to change this from opening gnome-terminal to opening terminator. , however these instructions do not appear to be valid any more, and I can't find any place in the system settings where the default emulator can be changed.  I also tried:  $ sudo update-alternatives --config x-terminal-emulator   choosing  * 0            /usr/bin/terminator               50        auto mode   But this does not appear to have any effect. Any idea how I can get this to work? When one should use spacing line \quad or \, PS4 Controller not connecting to PS4 and won't reset? I was playing my PS4 two days ago and then packed it up with two controllers that were both connected to this PS4.   I got to where I was going, set everything up and now the controllers won't connect. They show pulsing orange when they plug in, but when I hit the PS Button to connect, it blinks white 1-2 times and goes back to orange.   I have tried resetting them both.  Can anyone help? Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. Let $f$ be an entire function. Suppose $f(z)$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero. How to prove? Totally I have no idea... Please give the solution in detail since I do not understand. So one of this question's  answers got me curious. What is the maximum damage a 20th level character can do with a 9th level Magic Missile by the rules to a single target.  So my best I've been able to find is Aasimar or Goblin WLK 1/WIZ 19   9th Level slot (1D4+1)(11) [keep in mind you only roll once for damage not 11 times]  per  Empowered Evocation (+5)(11) (assuming 20 INT) Hexblade Curse (+6)(11) (Proficiency Bonus +6)    Radiant Soul/Fury of the Small +20 (Level 20 Aasimar/Goblin)   For a total of (D4+12)(11)+20 for (min-max)avg (163-196)179.5  Am I looking at this correctly? Are there other abilities out there that can increase this?  Feel free to include non legendary magic items. NO TOMES PLEASE  Only use things available on D&amp;D Beyond please.  Acceptable books are :   Basic Rules DMG, MM, PHB Sword Coast Adventure's Guide The Tortle Package Volo's Guide to Monsters Xanathar's Guide to Everything and any officially released Adventure Book The adjective ones I have heard recently are    forward straightforward forthcoming frank   I was wondering if each of them has positive, negative or neutral meaning?  What are other similar terms that are used for positive, neutral and negative intention? I am generating one report where I need to use background image. But I found that image always starts leaving some margin space to left side.    \documentclass{article} \usepackage{wallpaper} \usepackage{mdframed} \usepackage[top=2cm, bottom=2cm, outer=0cm, inner=0cm]{geometry} \begin{document}  Some content \ThisLRCornerWallPaper{1.0}{image.jpg} \end{document}    How can I use background image covering whole page? What is duplicate content and how can I avoid being penalized for it on my site? Show inline math as if it were display math (and vice versa) I'm very familiar with how symbols display differently in inline mode (with $ ... $) vs. how display math shows them (with \[ ... \] or $$ ... $$).  Two examples would be with limits  $\lim_{n\rightarrow \infty}f(x)$   vs.  \[ \lim_{n\rightarrow \infty}f(x) \]   and with sums  $\sum_{n=1}^{x} n^2$   vs.  \[ \sum_{n=1}^{x} n^2 \]   My Question is:     How do you display these things in inline mode (with all the nice inline formatting) as if they were in display mode ?   The inverse -- how to display things in display mode as if they were in inline mode -- is also of interest. Why can't I catch Pokemon in Pokemon Go anymore? I want to put a link to my SO profile on my homepage. I remember a codesnippet i saw somewhere that would basically display my Username and my reputation. Where was that? What are the eigenvalues of $\operatorname{ad}x$? Let $x\in \operatorname{gl}(n,F)$ have $n$ distinct eigenvalues $a_1,\ldots,a_n$ in $F$. Prove that the eigenvalues of $\text{ad }x$ are precisely the $n^2$ scalars $a_i-a_j$ ($1\leq i,j\leq n$), which of course need not be distinct.   So we can represent $x$ by an $n\times n$ matrix $X$. We have $Xv_1=a_1v_1,\ldots, Xv_n=a_nv_n$ for eigenvectors $v_1,\ldots,v_n$.   Now, $\operatorname{ad}x$ takes $y\in \operatorname{gl}(n,F)$ to $xy-yx$. I need to show that some $y$ is taken to a scalar multiple of itself, where that scalar is $a_i-a_j$. What could be that $y$? All of my Firefox add-ons have been disabled suddenly, how can I re-enable them? If you're interested in grammar, as I am, I am sure you have delved into a thought process about infinitive to, and like me, you have probably questioned what it is, or what it could be defined as. My mind always wants to place it in the Eight Parts of Speech, and I know this is foolish of me to some regard, so I stray from it, but I still wish to designate it under something that can be explain it. So, this is the motivation for this post, this question: What is the infinitive to, and why?  Here are my thoughts: There are three real possibilities, going back through the times. First, we can say that it is part of the verb that comes after it (to go, to run, etc.). This could be supported by the claim that you are not supposed to "split" infinitives ("To boldly go"), but only that.   Secondly, we could consider it a subordinator. I came across this designation most recently in my studies of modern and transformational grammar. As of right now, it is still the one I accept, especially as a result of the trend of designating more phrases as clauses. It works, except it's weird. Do we call this a unique subordinator as a result of how it operates? For example, to-infinitive clauses call for non-finite verb forms, which typically have an implied subject as a part of their clause. For example, "I want to go to the store." In the infinitive clause, "I" is the implied subject, as a understand. So, again, this works. However, things get a little weird when other subordinators come into play. For example, "I'm excited for you to win the competition." Now, if I'm right, those of you will say that "for" is a preposition here, as a result of the new-grammar stuff, but I'm going to count it as a subordinator, as defined by my own beliefs and that of a lot of other grammars. So, how do the clauses work in such a sentence? According to transformational grammar, "for you to win the competition" is defined as an ordinary clause. So, does that mean that it also contains a secondary clause within itself (the infinitive clause part)? If so, how do those two clauses work in conjunction to each other when one is so integrated? "For you to win the competition" looks to just be one clause, but if that's the case, doesn't "to" have to represent something else?  This moves us on to the third way to look at things, which is to consider "to" as auxiliary verb, a defective one at that. There are a lot of things to support this, and it even allows for the split infinitive. Furthermore, it calls for a non-finite verb form to follow, like an auxiliary. But, as I said before, it's defective in the way that is all it can function as.  As I said, I still accept to as a subordinator, but I want to be proven wrong or right. Wrong by showing evidence of it being something else, or right by showing how clauses operate when it seems to be layered up.