Javascript automatic variables from DOM IDs (2014)
Do DOM tree elements with ids become global variables?
Show that every connected graph with $n$ vertices has at least $n − 1$ edges.  How can I prove this?  Conceptually, I understand that the following graph has 3 vertices, and two edges:  a-----b-----c  with $a$, $b$ and $c$ being vertices, and $\{a,b\}$, $\{b,c\}$ being edges.  Is there some way to prove this logically?  --UPDATE--  Does this look correct?  Any advice on how to improve this proof would be appreciated.  Thank you. How do I migrate an SVN repository with history to a new Git repository? Is it possible to hide curves' guides in edit mode? Are the proofs for the properties of parallel lines, and that a triangle has 180 degrees, inherently tautological? I've noticed something while trying to prove the properties of parallel lines, and the properties that a triangle has 180 degrees. To prove the properties of parallel lines, such as alternate angles, you need to use the property that a triangle has 180 degrees. To prove a triangle has 180 degrees however, you need to use the properties of parallel lines. This really bothers me because of how circular it is. They are both reliant on each other to be true, and do not logically show, without being reliant on each other, why triangles have 180 degrees, and why parallel line properties are true.   So what I hoping for here is a way to prove parallel line properties without using the fact that a triangle has 180 degrees, or a way to prove triangles have 180 degrees without using parallel line properties. This way, things will be logical to me, and make sense.   Thanks in advance. This question came up after reading , in which it is re-iterated (as it has been many times on this site), that investing in the stock market, especially an index fund that tracks the top 100 / 500 companies in a country, basically always has great returns in the long run.  So my question is: Why isn't everybody rich?  If it is so easy (basically invest as heavily as you can in your youth to be rich into middle age and older), why doesn't everyone do this? There would be no need for pensions or any other savings or financial security that way, why even bother investing in assets like property that you have to manage when you can just have an index fund work for you?  I'm guessing that something is being missed here. I own a MicroMax A100. I want to install the latest version of a different ROM (Samsung or Nexus).  Is it possible? If so, can you tell me how?  If not, can I install a ROM made for a different device, but from the same manufacturer? For example, could I install a ROM for the MicroMax A110, which is the successor of A100? Questions about proving $\lnot \lnot a = a$ This is all in the context of a Hilbert system with modus ponens $A, A\to B \vdash B$ and axioms:  Axiom $1$: $A \to (B \to A)$   Axiom $2$: $(A \to (B \to C)) \to ((A \to B) \to (A \to C))$   Axiom $3$: $(\lnot B \to \lnot A) \to (A \to B)$  So I tried to prove double-negation elimination by doing the following:  \begin{array}{ccc} 1 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a &amp; \text{Premise}\\ 2 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a \to (\lnot \lnot \lnot \lnot a \to \lnot \lnot a)  &amp; \text{ Axiom } 1\\ 3 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot \lnot \lnot a \to \lnot \lnot a  &amp; \text{ Modus Ponens } 1, 2\\ 4 &amp; \{ \lnot \lnot a \} \vdash (\lnot \lnot \lnot \lnot a \to \lnot \lnot a) \to (\lnot a \to \lnot \lnot \lnot a)  &amp; \text{ Axiom } 3\\ 5 &amp; \{ \lnot \lnot a \} \vdash \lnot a \to \lnot \lnot \lnot a  &amp; \text{ Modus Ponens } 3, 4\\ 6 &amp; \{ \lnot \lnot a \} \vdash (\lnot a \to \lnot \lnot \lnot a) \to (\lnot \lnot a \to  a)  &amp; \text{ Axiom } 3\\ 7 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a \to  a  &amp; \text{ Modus Ponens } 5, 6\\ 8 &amp; \{ \lnot \lnot a \} \vdash a  &amp; \text{ Modus Ponens } 1, 7\\ 9 &amp; \vdash \lnot \lnot a \to a  &amp; \text{ Deduction Theorem } \\ \end{array}  And then I continued on, to prove double negation introduction:  \begin{array}{ccc} 10 &amp; \vdash \lnot \lnot \lnot a \to \lnot a &amp; \text{Double Negation Elimination}\\ 11 &amp; \vdash (\lnot\lnot \lnot a \to \lnot a) \to (a \to \lnot \lnot a) &amp; \text{ Axiom } 3\\ 12 &amp; \vdash a \to \lnot \lnot a &amp; \text{ Modus Ponens } 10, 11\\ \end{array}  My questions:   Am I allowed to invoke the deduction theorem in the middle of a proof like this (step $9$)? Is this considered a context change? Is context-changing allowed? Are the proofs even right/correct? Assuming it's all correct: Are we able to combine them to say that $a \to \lnot \lnot a$ and $\lnot \lnot a \to a$, therefore $a \iff \lnot \lnot a$ or is this symbol not allowed? What ultimately let us say $\lnot \lnot a = a$, the use of the equal sign here? Is Multiplying the Inverse Better or Worse? When dealing with double data types is multiplying by the inverse better or worse? Which way is faster? Which way uses less memory? Which way is preferred? How does MSIL handle this? SquareInches = MMSquared / 645.16  SquareInches = MMSquared * 0.0015500031000062000124000248000496    NB: 10K users will note that this is a duplicate of , which was deleted because the original question asker decided to berate everyone in the 'comments' section of the question.  This question was reposted because it is a 'good' question. Please 'uncheck' Community Wiki for your answer, as I'm only posting this as CW so that it's not seen as a 'reputation' grab. Related Question: int fn();  void whatever() {     (void) fn(); }   Is there any reason for casting an unused return value to void, or am I right in thinking it's a complete waste of time?  Follow up:   Well that seems pretty comprehensive.  I suppose it's better than commenting an unused return value since self documenting code is better than comments. Personally, I'll turn these warnings off since it's unnecessary noise.    I'll eat my words if a bug escapes because of it... Customize equation numbering for Equation environment? I want to manually label equation number ? For example I want to label this equation 3.1 instead of (1) which automatically pops up. Is it also possible in split environment as well or not ?      \begin{equation}     \log \mu_{ijk}= \lambda + \lambda_i ^I + \lambda_j ^J+\lambda_k ^K+\lambda_{ij} ^{IJ}+\lambda_{ik} ^{IK}+\lambda_{jk} ^{JK}+\lambda_{ijk} ^{IJK} \label{eq:3.1}     \end{equation} Merging two incoming broadband lines for faster Internet Multiplicative inverses for $Z_n$ Scale settings for exporting to STL (for 3d printing) I've set my Units (in scene properties) to Metric, and the Scene Scale to 0.01 hoping to get the Blender dimensions it mm's. While the (normal) scale is 1 for x,y,z, the standard cube has the dimensions 2x2x2 cm. When I export this to an STL and open it in a slicing program (Netfabb, Slic3r or Cura) they all give the dimensions: 2x2x2 mm. While exporting, the scale is 1.  What am I doing wrong? I hope you can help me.  Thanks! jQuery Datepicker with text input that doesn't allow user input How do I use the jQuery Datepicker with a textbox input:  $("#my_txtbox").datepicker({   // options });   that doesn't allow the user to input random text in the textbox. I want the Datepicker to pop up when the textbox gains focus or the user clicks on it, but I want the textbox to ignore any user input using the keyboard (copy &amp; paste, or any other). I want to fill the textbox exclusively from the Datepicker calendar.  Is this possible?  jQuery 1.2.6 Datepicker 1.5.2 Quaternion for beginner I have 2 points in 3d space ,point A= &lt;5,3,6> and B=&lt;8,2,3>  I want to rotate "point B" by 30 degree from point A.  how do I solve this question using quaternion.  Plz, explain the steps.... Calculating the expected values of the min/max of 2 random variables Installing mysql-workbench in Ubuntu 19.04 The error looks like this:  Reading package lists... Done Building dependency tree        Reading state information... Done Package mysql-workbench is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'mysql-workbench' has no installation candidate   How do I install it? How to place an image at the right top of a document? I've been learning LaTeX and this community has been very helpful. Currently, I'm trying to set up corporate letters but as a newbie I'm encountering a  of , so I'm posting them one by one instead of putting it in the comments... maybe this helps others as well.  Anyway, I am trying to implement this  that indicates that I can use vbox to float an image to the right of my header. I almost have this working, but I now try to adjust this to get my logo to stick to the top of the page. So I want to have this at the right top of my document. This is quite difficult! When I place the vbox, it creates unwanted spacing, for some odd reason. So I can not get the logo to be at the right top, even though I 'reset' every possible margin to 0 (in my opinion). Here is my distilled code:  \documentclass[a4paper]{article} \usepackage{graphicx} \graphicspath{{./img/}} \usepackage{color} \usepackage{xcolor} \definecolor{orange}{HTML}{DD4616} \definecolor{white}{HTML}{FFFFFF} \usepackage{fullpage} \usepackage[margin=0cm, paperwidth=215.9mm, paperheight=30mm,top=0cm]{geometry} \parindent=0pt  \begin{document} \fboxsep0pt  \pagecolor{orange}   \fbox{\vbox to 0pt{\hfill\fbox{\includegraphics[height=3cm]{logo}}}}  \end{document}   I've used a full black logo for illustrative purposes. Here you can see this:    The black line is the vbox border. For some reason, it jumps down. The only way to get rid of this that I found out about is this:    Which means that I need to add:  \edef\theprevdepth{\the\prevdepth}\nointerlineskip \vbox to 0pt{...}\prevdepth=\theprevdepth   But there are two problems with this:   I get an error with I try this (Improper \prevdepth.) More importantly, I really want to understand my code at this point, and get to master the basics of positioning elements. This feels overcomplicated and I do not understand it at all.    Is there any easy way to position an image at the right top of a document? What is the limiting factor in lens construction when it comes to f-stop values? How do Natures work? In at least some Pokemon games there are modifiers called "Natures" which affect pokemon stats. What do they do and how do it work? Also, what specific games possess it?