I was reading  because of another question on here, and I have read:     Her body had aged five centuries in its return to the present and, irreparably damaged   Which means that wizards can live over five centuries? Is there any more information on this?
In the Harry Potter series is it clear that magically-inclined individuals (witches/wizards) will live to be considerably older than their Muggle counterparts? From the question , it is given that Dumbledore was roughly 115 years old when he died, and at that age he hardly seemed ready to kick the bucket naturally.  With that in mind, how old will a wizard typically live to be, barring accidents or murder?
Cross referencing between chapters of a thesis Hi I am new to the forum and fairly new to Tex, if I miss anything out please let me know and I will be glad to post it. I am writing up my PhD thesis using Texmaker on a windows system. I have my document organised with a main file and a sub-directory containing chapter 1 to 5. I want to be able to use the labels I created in chapter two for example in the appendix and vice versa. Is there an easy way to do this?   I have tried following the advice of various posts of including the commands \usepackage{xr} and \externaldocument{Chapters/Chapter_2} in the individual chapters but this leads to an error when compiling.   My Preamble is as follows:  \documentclass[12pt,hidelinks,twoside]{report} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[greek,spanish,english]{babel} \usepackage{textgreek} \usepackage[version=3]{mhchem} \usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry} \usepackage{amsmath, amsfonts, pifont, float, color, url} \usepackage[pdftex]{graphicx} \usepackage[style=numeric,backend=biber,sorting=none]{biblatex} \addbibresource{references.bib} \usepackage[pdftex, plainpages=false, pdfpagelabels, bookmarks=true]{hyperref} \usepackage{fancyhdr} \usepackage[center,font={it,small}]{caption}   I then have a section such as this in the main document:  \begin{document} %%... Title page ... \chapter{Theory and Methods} \label{chap:Theory and Methods} \include{Chapters/chapter_2} %%... Other chapters .... \end{document}   In Chapter 2 I have for example a label for a diagram which I may want to reference in other chapters:  \begin{figure}[H] \centering \includegraphics[height=10cm,width=\textwidth]{RF_colour_hi_res.pdf} \caption{Random Forest} \label{fig:2.1 Random Forest} \end{figure}   How can I have this label show up in other chapters after I type \ref ?  Many thanks in advance.  If any other information is required please let me know.   This has been answered in the comments although the references do not appear in the auto complete if they are copied and pasted in they still work. How to input a specific Pantone color number in Illustrator? Is an expanding map on a compact metric space continuous? I got inspired by this question  to think about the following problem: Suppose you have a compact metric space $(X,d)$ and an expanding map $T:X\rightarrow X$, i.e. $d(Tx,Ty)\geq d(x,y)$ for every $x,y\in X$. Is the map $T$ then continuous? Without assuming continuity we already know that $T^n(X)$ must be dense in $X$ for any $n\geq 1$, since given $z\in X$ the orbit of $z$ must accumulate upon $z$. But showing continuity has escaped me so far. If there are counter-examples using the Axiom of Choice that also interests me. On a series involving harmonic numbers How to determine if .NET code is running in an ASP.NET process? I have an instance of a general purpose class that will be executed both under ASP.NET and a stand alone program. This code is sensative to the process where it is being run - that is, there are certin methods that should not called if running under ASP.NET. How do you determine if the code is executing in an ASP.NET process?  The solution I am currently using is answered below.    I wish someone would add a comment as to why this question has gotten downvoted and/or propose a better way to ask it! I can only assume at least some folks have looked at the question and said "what an idiot, ASP.NET code is .NET code". Phase Potentials Looking to get a explanation of the following solution.   $x'=sinx$ I understand that you must integrate $sinx$ and then take the negative of it making it $v(x)=cos(x) + c = cos(x)$ with $c=0$. However I am having problems understanding the equilibrium points.   The equilibrium points of this system are,  $$x^*=kz$$ $x*=kz$ k is even, this is unstable $x^*=kz$ k is odd, are stable  Why is it unstable when even and stable when even? The merits of a partitionless filesystem I ran into something a couple of weeks ago that I'd never seen before: A filesystem (ext3 I believe) installed to a storage device without a partition. In essence /dev/sdb was the entire filesystem. I know many filesystems can be extended into empty space, so doing this allows extending without dealing with LVM or some other kind of volume manager, but are there any other advantages for setting up storage this way?  The specific case I saw was as the ephemeral data volume for a number crunching server, the boot and root volumes were traditional partitions on a different storage device entirely. - Which one is correct, or are both of them fine?    "It would take the average person 10 days to read this novel"    Or    "It would take an average person 10 days to read this novel" Are commands complete sentences? seems to indirectly ask the question, but the upvoted answer says &quot;the actual sentence is...&quot;. So my question is this: Are commands considered to be grammatically sound, complete sentences in the English language? Some examples:  Go. Add a note. Do work. What is a glue record? This is a  about DNS glue records.   What exactly (but briefly) is a DNS glue record?  Why are they needed and how do they work? Possible Duplicate:          Well, the question is in the title. I always had the impression that "talk to someone" refers to situations when some information must be conveyed to someone else, while "talk with someone" refers to cases that involve a more complex two-sided interaction. E.g., I "talk to my colleague" to tell him that I'm going for a lunch break (no response is required apart from maybe an acknowledgment), while I go and "talk with my colleague" if I have to discuss something with him in detail. Is this correct, or is there any difference between the two phrases, or is there no difference at all? To prove $\sum_{cyc}\frac{1}{a^3+b^3+abc} \le \frac{1}{abc}$ if $a,b,c$ are non zero positive reals prove $$\sum_{cyc}\frac{1}{a^3+b^3+abc} \le \frac{1}{abc}$$ I have used A.M  G.M  inequality as follows:  $$a^3+b^3+c^3 \ge 3abc$$ adding $abc$ both sides we get  $$a^3+b^3+abc \ge 4abc-c^3=c(4ab-c^2)$$ so  $$\frac{1}{a^3+b^3+abc} \le \frac{1}{c(4ab-c^2)}$$ But since $a,b,c$ are positive reals  $$4abc-c^3 &lt; 4abc$$ so  $$\frac{1}{4abc-c^3} \gt \frac{1}{4abc}$$  but i am unable to proceed here Can Mjolnir be lifted & wielded by anyone if Thor is touching it? In The Big Bang Theory episode , Penny, Amy, and Bernadette are having an argument if Thor's hammer:   Can be lifted by anyone in space.     Can be lifted &amp; wielded by anyone if Thor is touching it.   The first argument is settled in .  But the second argument remains unsolved.  Can Thor's hammer be lifted &amp; wielded by anyone if Thor is touching it? Is there a dollar amount that, when adding Massachusetts Sales Tax, precisely equals $200? Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer. Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.   I'm not familiar to factorial and I don't have much idea, can someone show me how to prove this? Thank you. I understand that the vibration modes of an elementary string determines the identity of its particle. When I first heard this, I visualized a stiff circular steel band-like entity vibrating with 2, 3, 4, 5,... nodes or antinodes, the number determining the particle. This was further supported when I asked a well-known physicist how one gets from equations to physical strings, and he said he recognized the harmonic nature of the solutions.  Bu then I noticed that physicists seem to accept the image of a soft spaghetti-like string flopping about with no well-defined vibrational modes. I asked another physicist about this, and his answer was simply that a string has multiple modes, not necessarily in a harmonic progression.  So my questions are 1) How do you visualize the vibrations of a string, and 2) how are they related to particle identity? proof of functional completeness of logical operators If I know that the set of operators {∨, &amp; , ¬} is functionally complete, how do I go about proving/disproving the functional completeness of the following set of operators?  a) $\{\vee,\neg\}$  b) $\{\to,\neg\}$  c) $\{\to\}$  I have looked at the answer here for (b) : How can I calculate magnification ratio I get by reversing a lens? I am looking for a way to mathematically determine the maximum magnification ratio that is possible/practical to achieve by reverse mounting a non-macro lens, prior to purchasing the lens.     See related questions: Run a GUI program at startup I am using Ubuntu 14.04. I wrote a small script named trial. The contents of the script are as follows:   #!/bin/sh SHELL=/bin/sh PATH=/bin:/sbin:/usr/bin:/usr/sbin      sh -c firefox   I copied the script to /etc/init.d, modified permission using chmod +x trial and used update-rc.d trial defaults. The file made link but when I rebooted the machine. It did not run firefox. I tried cron @reboot but with no success. I tried rc.local too again failure. Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution. $$(z+1)^6=z^6 $$ $$\frac{(z+1)^6}{z^6 }=1$$ $$\left(\frac{(z+1)}{z }\right)^6=1$$ $$\left(\frac{(z+1)}{z }\right)^6=\cos(2*\pi*k)+i\sin(2*\pi*k)$$ $$\frac{(z+1)}{z }=\left(\cos(2*\pi*k)+i\sin(2*\pi*k)\right)^{1\over6}$$ $$1+\frac{1}{z }=\cos({2*\pi*k\over6})+i\sin({2*\pi*k\over6})$$  $$\frac{1}{z }=(\cos({\pi*k\over3})-1)+i\sin({\pi*k\over3})$$ $$\frac{1}{(\cos({\pi*k\over3})-1)+i\sin({\pi*k\over3}) }=z$$ I dont know how else to solve this. A lot of help is appreciated. Also i know that k should go from 1-5.