Bug or limit of Delphi's max. constant integer values?
E2099 Overflow in conversion or arithmetic operation
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$ Using only rules of natural deduction, I am trying to prove that $$p \implies q \vdash \lnot p \lor q$$ but am having a lot of difficulty. I was able to prove the other direction.   Could anyone show me or point me to the right direction? Windows 10 upgrade led to grub rescue Due to my ignorance, I find that most of the references for mathematical analysis (real analysis or advanced calculus) I have read do not talk much about the "multivariate calculus". After dealing with the single variable calculus theoretically, it usually directly goes to the topic of measure theory.    After reading the wiki article "", I'd like to find the rigorous proof for this test. The first book comes to my mind is Courant's Introduction to Calculus and Analysis which includes the multivariate case in the second volume.   Motivated by this, I'd like to put the question here:     What are the usual references for the   theoretical treatment for   ? The equivalent electric field of a magnetic field I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by  $$\vec{F} =q \vec{v} \times \vec{B}$$  but there will exist a frame of reference where observer move at same velocity with that of charge $q$, so according to him $v=0$. hence he will see no magnetic force is exerted on charge $q$. I have work on this problem for a while and found that the special relativity predicts equivalent electric force will acting upon charge instead. I want to know the relationship between this equivalent electric force and magnetic force.  Thanks in advance Expansion of $(1+\sqrt{2})^n$ My friend and I were discussing this and we couldn't figure out how to prove it one way or another.  The only rational values I can figure out for $\sin(x)$ (or $\cos(x)$, etc...) come about when $x$ is some product of a fraction of $\pi$.  Is $\sin(x) $ (or other trigonometric function) necessarily irrational if $ x $ is rational?  Edit: Excluding the trivial solution of 0. I want to filter a java.util.Collection based on a predicate. Word: how to show hidden ribbon tabs? How can I control which tabs are available to be opened in the MS Word 2010 ribbon?  Under Word Options > Customize Ribbon > Main Tabs there are several groups checked (Blog Post, Insert (Blog Post), Outlining, Background Removal), but they don't appear on the ribbon even though there is space for them. How is one supposed to turn them on or get to them?  The one in particular I'm after today is the Blog Post tab, which I know I can get to in a round about way via File > New > Blog Post Template. However I don't want a new post, rather an old one, which means File > New > Blog Post Template > Open existing > [select from list] > [close new blog post window] > [slap No I don't to save darn it]. Extra work for nothing is irritating; how do I get Blog Post (or Outlining or ...) to show up in that nice empty space next to AddIns? Beta regression of proportion data including 1 and 0 Is there something like python's interactive REPL mode, but for Java? Is there something like python's interactive REPL mode, but for Java? So that I can, for example, type InetAddress.getAllByName( localHostName ) in a window, and immediately get results, without all this public static void nightmare() thing? Play YouTube videos with MPMoviePlayerController instead of UIWebView Consider $\mathbb R^{[0,1]}$ the space of all functions from $[0,1]$  to $\mathbb R$  and the cylindrical sigma algebra $\mathcal B$  on it. The question is: how to prove that $C[0,1]\notin \mathcal B$. Why can't light escape from a classical black hole? What is information? If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$ How to make Table of Contents manually I'm trying to make table of contents manually, I mean I set the page of each of sections one by one. Here's my target:  and I'm using book class here.  Here's the code that I found   \documentclass[oneside]{book} \renewcommand\contentsname{CONTENTS} \renewcommand\listtablename{LIST OF TABLES} \renewcommand\listfigurename{LIST OF FIGURES} \addtocontents{toc}{{\bfseries Contents\hfill Page No.\bigskip\par}} \addtocontents{lot}{{\bfseries No.\hfill Title\hfill\hfill Page No.\bigskip\par}} \addtocontents{lof}{{\bfseries No.\hfill Title\hfill\hfill Page No.\bigskip\par}}  \usepackage[titles]{tocloft} \usepackage{xcolor,xpatch} \renewcommand\cftbeforechapskip{0ex} \renewcommand\cftchapfont{\mdseries} \renewcommand\cftchappagefont{\mdseries} \renewcommand\cftchappresnum{Chapter~} \renewcommand\cftchapaftersnum{. } \newlength\tocindent \settowidth\tocindent{\cftchapfont\cftchappresnum9\cftchapaftersnum} \edef\cftchapnumwidth{\the\tocindent} \edef\cftsecindent{\the\tocindent} \advance\tocindent2.3em \edef\cftsubsecindent{\the\tocindent} \advance\tocindent3.2em \edef\cftsubsubsecindent{\the\tocindent} \renewcommand\cftsecdotsep{\cftnodots} \renewcommand\cftsubsecdotsep{\cftnodots} \renewcommand\cftsubsubsecdotsep{\cftnodots} \newcommand\tocmainmatter {\renewcommand\cftchappagefont{\color{white}}% } \xapptocmd\mainmatter{\addtocontents{toc}{\protect\tocmainmatter}}{}{}   \newif\ifschaptertoc \makeatletter \renewcommand\@makeschapterhead[1]% {{\parindent \z@ \centering     \normalfont     \interlinepenalty\@M     \Large \bfseries  #1\par\nobreak     \vskip 20\p@ }% \@mkboth{\MakeUppercase{#1}}{\MakeUppercase{#1}}% \ifschaptertoc \addcontentsline{toc}{chapter}{#1}% \fi } \makeatother  \usepackage{blindtext}  \begin{document} \frontmatter  \tableofcontents \schaptertoctrue  \chapter*{ACKNOWLEDGEMENTS} \blindtext  \chapter*{ABSTRACT} \blindtext  \listoftables  \listoffigures  \chapter*{ABBREVIATIONS} \Blindtext  \chapter*{NOTATIONS} \Blindtext  \mainmatter  \chapter{INTRODUCTION} \blindtext  \section{General Background} \blindtext  \section{Objective} \blindtext \subsection{Objective 1} \blindtext \subsection{Objective 2} \blindtext \subsection{Objective 3} \blindtext  \section{Scheme} \blindtext \end{document} Viruses: Adaptation to a new host through repeated host jumps A friend told me, during a 3 minute discussion, that viruses that are endemic in host $A$ and make repeated jumps to host $B$ but can't be transmitted between individuals of species $B$, may slowly adapt (through these repeated jumps) to be able to be transmitted between individuals of host $B$ and become epidemic.  I don't know much about epidemiology. I don't understand how a virus population that is endemic to host $A$ may adapt to host $B$ with repeated jumps while the viruses that jump to host $B$ are dead end because they cannot be transmitted further more. Or Are these viruses able to jump back to host $A$ to bring back their newly acquired adaptations to host $B$?  Also, I might misunderstand the meaning of "repeated host jumps transmission". I first thought it meant repeated jumps from a reservoir population in host $A$ to host $B$, but it is also possible that it describes the dynamic of a virus population that is adapted to jump from species to species and they actually gain this ability by keeping jumping and jumping. But then, how could a virus species get adapted to jump from species to species? I'm a bit confused…. Can you give me some hints about this process of cross-species transmission through repeated jumps? What it's the best way to generate a string of \t's in C#  I am learning C# and experimenting with different ways of saying the same thing.    Tabs(uint t) is a function that returns a string with t amount of \t's  For example Tabs(3) returns "\t\t\t"  Which of these three ways of implementing Tabs(uint numTabs) is best?  Of course that depends on what "best" means.     The LINQ version is only two lines, which is nice.  But are the calls to Repeat and Aggregate unnecessarily time/resource consuming? The StringBuilder version is very clear but is the StringBuilder class somehow slower? The string version is basic, which means it is easy to understand.   Does it not matter at all?  Are they all equal?   These are all questions to help me get a better feel for C#.     private string Tabs(uint numTabs) {     IEnumerable&lt;string&gt; tabs = Enumerable.Repeat("\t", (int) numTabs);     return (numTabs &gt; 0) ? tabs.Aggregate((sum, next) =&gt; sum + next) : "";  }    private string Tabs(uint numTabs) {     StringBuilder sb = new StringBuilder();     for (uint i = 0; i &lt; numTabs; i++)         sb.Append("\t");      return sb.ToString(); }    private string Tabs(uint numTabs) {     string output = "";     for (uint i = 0; i &lt; numTabs; i++)     {         output += '\t';     }     return output;  } Zooming in to inspect texture details in 3D view clips some closer faces like shown in the image. It's not the camera view so changing camera settings doesn't help.   Where can the distance to the clipping plane be adjusted? A Linear Diophantine Equation is of the following form:                                                                                        $Ax+By+C=0$, where $x_1 \leq x \leq x_2$ and $y_1 \leq y \leq y_2$.  If the value of $A,B,C,x_1,x_2,y_1,y_2$ are given and $x_1 \leq x_2$ and $y_1 \leq y_2$, then how many solutions can be found? How can I find out the total number of solutions according to the above condition.