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So basically , we all know the direction outside the magnet its from NORTH to SOUTH. but what i don't understand is that what is the direction inside is it the same ?? How can I get two Xbox 360's to be in "open nat" mode behind the same router? I have two Xbox 360's, one WiFi and the other wired through the same Linksys E3000 router with DD-WRT (v24-sp2 (04/13/11) std-usb-nas firmware).   Mine (the wired one, though hers has been wired in the past and it didn't appear to help) always seems to be open (green), and hers is either moderate or closed (oj/red)  Even with the original router firmware I've never been able to get both consoles into "open nat" mode, and it makes playing certain games together almost impossible for me and my wife  because we can't seem to get into the same game.   I have uPnP enabled and the DMZ disabled, and some minor port forwarding to allow for a Minecraft server (Ports 25565 and 25566 for a testing copy of the server), but other than that the settings are mainly at their default, on the xbox's and the router.   Are there any settings I can configure to allow this to work properly? Could someone provide me with a good explanation of why $0^0=1$?  My train of thought:  $x&gt;0$  $0^x=0^{x-0}=0^x/0^0$, so  $0^0=0^x/0^x=\,?$  Possible answers:   $0^0\cdot0^x=1\cdot0^0$, so $0^0=1$ $0^0=0^x/0^x=0/0$, which is undefined   PS. I've read the  on mathforum.org, but it isn't clear to me. LaTeX: optional arguments with square brackets LaTeX is trying to add a missing $ that I don't want to the following code. Minimal working example:  \documentclass[letter,12pt]{article}  \newcommand{\monkeyBeans}[2][]{   \parbox{4in}{#1} }  \begin{document}  \parbox{4in}{$[a, b]$}   \monkeyBeans[$[a, b]$]{yo monkey}  \end{document}   If I try any of the following lines in my document instead of the call to monkeyBeans, there is no error:  \parbox{4in}{$[a, b]$}  \monkeyBeans[yo monkey]{$[a, b]$} \monkeyBeans[$(a, b)$]{yo monkey} \monkeyBeans{$[a, b]$}{yo monkey}   What is the deal with square brackets in optional arguments? How does Cantor's diagonal argument work? I'm having trouble understanding Cantor's diagonal argument.  Specifically, I do not understand how it proves that something is "uncountable".  My understanding of the argument is that it takes the following form (modified slightly from the  article, assuming base 2, where the numbers must be from the set $ \lbrace 0,1 \rbrace $):  \begin{align} s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In this case, the diagonal number is the bold diagonal numbers $(0, 1, 1)$, which when "flipped" is $(1,0,0)$, neither of which is $s_1$, $s_2$, or $s_3$.  My question, or misunderstanding, is: When there exists the possibility that more $s_n$ exist, as is the case in the example above, how does this "prove" anything?  For example:  \begin{align} s_0 &amp;= (1,0,0,\mathbf{0},\dots)\ \ \textrm{ (...the wikipedia flipped diagonal)}\\ s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ s_4 &amp;= (0,1,1,\mathbf{1},\dots)\\ s_4 &amp;= (1,0,0,\mathbf{1},\dots)\ \ \textrm{ (...alternate, flipped } s_4\textrm{)}\\ s_5 &amp;= (1,0,0,0,\dots)\\ s_6 &amp;= (1,0,0,1,\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In other words, as long as there is a $\dots \text{ continues}$ at the end, the very next number could be the "impossible diagonal number", with the caveat that it's not strictly identical to the "impossible diagonal number" as the wikipedia article defines it:     For each $m$ and $n$ let $s_{n,m}$ be the $m^{th}$ element of the $n^{th}$ sequence on the list; so for each $n$,      $$s_n = (s_{n,1}, s_{n,2}, s_{n,3}, s_{n,4}, \dots).$$      ...snip...      Otherwise, it would be possible by the above process to construct a sequence $s_0$ which would both be in $T$ (because it is a sequence of 0s and 1s which is by the definition of $T$ in $T$) and at the same time not in $T$ (because we can deliberately construct it not to be in the list). $T$, containing all such sequences, must contain $s_0$, which is just such a sequence. But since $s_0$ does not appear anywhere on the list, $T$ cannot contain $s_0$.      Therefore $T$ cannot be placed in one-to-one correspondence with the natural numbers. In other words, it is uncountable.   I'm not sure this definition is correct, because if we assume that $m = (1, \dots)$, then this definition says that "$s_n$ is equal to itself"&mdadsh;there is no "diagonalization" in this particular description of the argument, nor does it incorporate the "flipping" part of the argument, never mind the fact that we have very clearly constructed just such an impossible $T$ list above.  An attempt to correct the "diagonalization" and "flipping" problem:  $$s_n = (\lnot s_{m,m}, \lnot s_{m,m}, \dots) \quad \text{where $m$ is the element index and} \quad\begin{equation}\lnot s_{m,m} = \begin{cases}0 &amp; \mathrm{if\ } s_{m,m} = 1\\1 &amp; \mathrm{if\ } s_{m,m} = 0\end{cases}\end{equation}$$  This definition doesn't quite work either, as we immediately run in to problems with just $s_1 = (0),$ which is impossible because by definition $s_1$ must be $ = (1)$ if $s_1 = (0)$, which would also be impossible because...   Or more generally, with the revised definition there is a contradiction whenever $n = m$, which would seem to invalidate the revised formulation of the argument / proof.  Nothing about this argument / proof makes any sense to me, nor why it only applies to real numbers and makes them "uncountable". As near as I can tell it would seem to apply equal well to natural numbers, which are "countable".  What am I missing? What's wrong with this argument that $[0,1]$ is countable? When to use a hyphen to coin a new word and when to omit a hyphen? Someone has asked for answer to these topics. However, I still want someone to provide me with simple and universal answers. I recently read a sentence from the English-speaking person. It is in an article. It is, ' The available options for mitigating pad cratering are not universally effective (see link below), but they may be helpful on a case by case basis until more crack resistant laminates are developed and become available.  '  If I am to write this, I will use 'a case-by-case basis until more crack-resistant laminates'   Can anyone tell me when to use a hyphen to coin a new word? Is it possible to insert arguments into functions when they're used like Function@ or //Function? LaTeX Error: Option clash for package xcolor I have an option clash between package xcolor and another package, but I don't know which. Here is my MWE  \documentclass[10pt]{beamer} \setbeamertemplate{navigation symbols}{} \usepackage{caption} \usepackage{subcaption} \usepackage{url} \usepackage{color} \usepackage[usenames]{xcolor}  \author{The author} \title{Package conflicts} \date{October 3rd, 2012}  \begin{document}  This is supposed to be \textcolor{olivegreen}{olivegreen} \end{document}   And the error message is :  This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) entering extended mode (./error_xcolor.tex LaTeX2e &lt;2009/09/24&gt; &lt;blablabla&gt; ! LaTeX Error: Option clash for package xcolor.   I hope this is enough log for you guys. At this time of the day, I'm hoping for America to save my french ass ... again : ) How to display random jokes from www.icndb.com in your terminal? I already know that you can get some nice quotes/jokes using the  program.  But I've found in this  a new source of fun that I'd like to have when I open a new terminal.  This time the jokes come from . Free ornaments font I'm looking for a free ornaments font. I know about  and pifont. Where can I find more glyphs? My laptop has a function key which turns F keys into keys which change volume or brightness. I would like to swap a number of them so that they perform that function under normal operation and are an Fx key while the function key is being held.  I assumed that the function keys were just normal keys codes with the set of keys being large enough to include all the possible speical keys. I tried to so as this tutorial suggests () and use xev to obtain the key codes and then would use xmodmap to swap their value.  This does not seem to work though. The F12 key gives the xev output:  KeyPress event, serial 41, synthetic NO, window 0x4a00001,     root 0xb1, subw 0x0, time 468005, (23,-15), root:(89,37),     state 0x10, keycode 96 (keysym 0xffc9, F12), same_screen YES,     XLookupString gives 0 bytes:      XmbLookupString gives 0 bytes:      XFilterEvent returns: False   Which I think is to be expected. However, the Increase Volume button give this response:  KeymapNotify event, serial 41, synthetic NO, window 0x0,     keys:  65  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0               0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0    And so does the Decrease Volume key. How can I perform the swapping of the keys that I would like?  Thank you Is $\frac{1}{\sqrt{2}}$ a fraction or not?   I just came across a Grade 8 student's class work where the teacher has given the above as an example to differentiate fractions from rational numbers. I think this is wrong fundamentally, as $\sqrt2$ is irrational while all fractions would be rational. Please advise. Thanks! Unfortunately, I need to do this.  I'm using ELMAH for my error log.  Before I route to my error.aspx view, I have to grab the default ELMAH error log so I can log the exception.  You used to be able to use   Elmah.ErrorLog.Default   However, this is now marked as obsolete.  The compiler directs me to use the method  Elmah.ErrorLog.GetDefault(HttpContext context)   MVC's context is of type HttpContextBase, which enables us to mock it (YAY!).  How can we deal with MVC-unaware libraries that require the old style HttpContext? wp_customize_image_control default value Is it possible to use more than 20 layers? Is it possible to use more than 20 Scene layers or Render layers in Blender? The disk that contains Ubuntu on my computer is 115GB in size.  When the disk was 114.7GBfull.  I started deleting some files here and there to free up around 5GB.  But I noticed the disk was 114GB filled again. I thought it was some cache or swap thingy so didn't give it much thought and went ahead and freed around 40GBby shifting some media files out of the disk.  I have a notification in an hour or so that the disk is full yet again!! 40GB!!! All gone!  So I debugged the problem down to the /var/log/syslog file which was initially definitely less than 20GB. I know this because /var folder was 17GB before I cleared the memory.  /var/log/syslog file is currently 55.9GB!  Could someone be so gracious to explain this anomaly? Is this a bug? Or am I affected with some malware or virus? Empty set does not belong to empty set Herbert in his book "Elements of set theory" on page no 3 says that      we can form the set $ \{ \emptyset \} $ whose only member is $\emptyset $. Note that $ \{ \emptyset \} \neq  \emptyset $, because $ \emptyset \in \{ \emptyset \} $ but $\underline{ \emptyset \notin \emptyset} $·   By the last argument $\emptyset \notin \emptyset$, is he saying that empty set is not a member of or does not belong to empty set  OR  it is a typo and he wanted it to be $ \{\emptyset \} \notin \emptyset $, that set containing empty set is not a member of empty set What's the standard "roadmap" to learning quantum physics? I'm really interested in quantum physics and would like to learn more. However, I don't know where to start and in what order I should learn things. So, ideally I'm looking for some sort of roadmap of what to learn. What physics topics do I need to know to start learning about quantum mechanics? (In addition to the mathematical topics mentioned at )  My current knowledge is mostly popular science stuff, like tv shows on Discovery Science and National Geographic Channel. So I have a basic understanding of some basic principals. There's also a recent lecture from Brian Cox that I have watched which gave a bit more in-depth information. I heard the following dialog in a British English movie:     Words go round quick. All the little tongues go clack, clack, clack.   What does this mean, and why was the word "quick" used instead of "quickly"?