I'd like to create a partition where to install Ubuntu in a Dell inspiron 6000 with WinXp OS already installed. What is the minimal amount of disk space required for booting the system? Then I'd create another partition for the data.  I tried to install Ubuntu alongside WinXP without creating a dedicated partition but the grub install failed at the end.
I know how much space is required to install Ubuntu.  How much space does a Ubuntu installation take up on the disk?
I've been very into acoustics lately, specifically the harmonic series. I find it fascinating how the harmonic series works as a sort of guideline to harmony, and how we base tuning systems on trying to estimate the intervals from the harmonic series.  As you've probably gathered already, I know close to nothing about acoustics. But I would love an acoustic textbook that's suitable for dummies like myself. Is it safe to use oil at its smoking point? Teflon toxicity and second degree burns aside, are there any health issues related to cooking with oil at or past its smoking point? Googling a bit I found one article that went so far as to say you should always "discard oil that's reached its smoke point, along with any food with which it had contact". Other searches showed pages suggesting cancer risks.  I've never given it a thought before and I often use peanut oil at smoking point to brown meat. Why: a relative adverb, a conjunction ... or both? I am not familiar with the idea that an adverb can function as a conjunction at the same time. Here are a couple of sentences that are confusing me.     This is the reason why she left him.   ...and     He was transferred to New York, where he was promoted to a higher level.   The  why, where, when, and how seem to introduce a clause. Therefore, can they also be called conjunctions? If yes, would I be right in assuming that relative adverbs can function as conjunctions at the same time? Can sum of a rational number and its reciprocal be an integer?   My brother asked me this question and I was unable to answer it.   The only trivial solutions which I could think of are $1$ and $-1$.  As to what I tried, I am afraid not much. I have never tried to solve such a question, and if someone could point me in the right direction, maybe I could complete it on my own.  Please don't misunderstand my question.   I am looking for a rational number $r$ where $r + \frac{1}{r}$ is an integer. Elementary properties of closure Hi everyone I'd like to know if the following is correct. I really appreciate any suggestion. (Honestly the only one that matters me is the second property the others are easy, I think) Thanks.  Definition: Let $X\subset \mathbb{R}$ and let $x'\in \mathbb{R}$, we say that $x'$ is an adherent point of $X$ iff $\,\forall\varepsilon&gt;0\,\exists x\in X \text{ s.t.} \; d(x',x)\le \varepsilon$. We say that $\overline{X}$ is the closure of $X$ iff contain all the adherent points of $X$.  Lemma (Elementary properties of Closures): Let $X$ and $Y$ be arbitrary subset of $\mathbb{R}$. Then $X\subset \overline{X}, \; \overline{X\cup Y}=\overline{X}\cup\overline{Y},\; \overline{X\cap Y}\subset\overline{X}\cap\overline{Y}$. If $X\subset Y$ then $\overline{X}\subset \overline{Y}$.  Proof:  Clearly if $x\in X$,  $x$ is $\varepsilon$-adherent to $x$ (indeed is $0$-close to itself) for every $\varepsilon$, hence $x\in \overline X$.   Let $z'$ be an adherent point of $X\cup Y$, then there exists some $z\in X\cup Y$ such that $d(z',z)$ for a given $\varepsilon&gt;0$. Suppose  $z\in X$, hence $z'$ is an adherent point of $X$, i.e., $z'\in \overline{X}\subset \overline{X}\cup \overline{Y}$. Similarly when  $z\in Y$, $z'\in \overline{Y}\subset \overline{X}\cup \overline{Y}$. Thus $ \overline{X\cup Y}\subset\overline{X}\cup \overline{Y}$. We  know that $X\cup Y \subset\overline{X\cup Y}\subset\overline{X}\cup \overline{Y}$. Then $\overline{\overline{X\cup Y}}=\overline{X}\cup \overline{Y}$. Since $\overline{\overline{X\cup Y}} = \overline{X\cup Y}$ we're done.  Let $z'\in \overline{X\cap Y}$, i.e., $z'$ is an adherent point of $X\cap Y$. So, there is some $z\in X\cap Y \subset X$ such that $d(z',z)\le \varepsilon$ for any given $\varepsilon&gt;0$. It follows that $z'$ is an adherent point of $X$, i.e., $z'\in \overline{X}$. Similarly since $z\in X\cap Y \subset Y$ we have $z'\in \overline{Y}$. Hence $z'\in \overline{X}\cap\overline{Y}$.   Let $x'\in \overline{X}$ we'd like to show that $x'\in \overline{Y}$. Let $\varepsilon&gt;0$ be arbitrary then $\exists x\in X\subset Y$ such that $d(x',x)\le \varepsilon$, so $x'$ is an adherent point of $Y$, i.e., $x'\in \overline{Y}$ as desired. $\Box$     Claim 1: If $X\subset Y \subset \overline{X}$. Then $\overline{Y}=\overline{X}$.    Proof claim: Let $y'$ be an adherent point of $Y$, i.e., $y'\in \overline{Y}$ and let $\varepsilon&gt;0$ be given. Thus, $\exists y \in Y\subset \overline{X}$ s.t. $d(y,y')\le \varepsilon$. So, $y$ is an adherent point of $X$. Thus $\exists x\in X$ s.t. $d(x,y)\le \varepsilon$ and therefore  we must have $d(x,y')\le 2\varepsilon$ which shows that $y'$ is an adherent point of $X$, i.e., $\overline{Y}\subset \overline{X}$. Conversely if $x'$ is an adherent point of $X$. Then $\exists x\in X\subset Y$ s.t. $d(x,x')\le \varepsilon$, and so is adherent to $Y$. $\Box$     Claim 2: $\overline{\overline{X}} = \overline{X}$    Proof: It will suffice to show that if $x''\in \overline{\overline{X}}$, then $x''$ is an adherent point of $X$. Let $\varepsilon &gt;0$ be arbitrary and let $x''$ be an adherent point of $\overline{X}$. Then there is some $x' \in \overline{X}$ such that $d(x'',x')\le \varepsilon$. Since $x' \in \overline{X}$ by definition is an adherent point of $X$, so there is some $x\in X$ for which $d(x,x')\le \varepsilon$. Thus $d(x,x'')\le d(x,x')+d(x',x'')\le 2\varepsilon$ it follows that $x''$ is an adherent point of $X$ as desired. $\Box$ I wonder about the foundations of set theory and my question can be stated in some related forms:   If we base Zermelo–Fraenkel set theory on first order logic, does that mean first order logic is not allowed to contain the notion of sets? The axioms of Zermelo–Fraenkel set theory seem to already expect the notion of a set to be defined. Is there are pre-definition of what we are dealing with? And where? In set theory, if a function is defined as a set using tuples, why or how does first order logic and the axioms of Zermelo–Fraenkel set theory contain parameter dependend properties $\psi(u_1,u_2,q,...)$, which basically are functions? Template Hierarchy: confused with index.php, front-page.php, home.php I'm really confused with index.php, home.php and front-page.php. In many cases even though I had an index.php, I overwrite it with front-page.php. But recently, I became aware about home.php.   What's the difference between the home.php and index.php? What's the ideal condition to use a home.php than an index.php? What's the ideal condition to use a front-page.php? When I'm using a front-page.php then what specific task an index.php is doing for me then?   I've read the  in Codex. Please don't mix my question with Page Templates, I understand 'em, alHamduLILLAH. Is there a gender-neutral pronoun that can replace “his” or “her”? Best technique to create oldschool (fake 3D) racing game? What would be a good approach to develop the render system for an oldschool type racing game that uses a pseudo 3D scenery, like for example Outrun or Lotus Esprit Turbo Challenge? There's an endless scrolling road and scenery graphics are placed like billboard items, etc. I think you get the idea.    Are these developed in a similar way like  or is there a different technique behind it? Does the technique has a specific name I could search for on the web? I need to develop something like that in Flash. How to remove or hide the GRUB boot menu? Recently I decided to use only Ubuntu and there is no Windows in my laptop. When I turn on my laptop the GRUB menu is showing but I don't need to choose OS anymore.   How can I remove or hide this? And after removing this how could I access to recovery mode? I am flying from New Orleans to Dulles (IAD) on United Express, and from IAD to Frankfurt on United. I have a short connection (45 minutes) in IAD.   I'm trying to figure out how can I make it:  Will I need to go throughout security and border check since I'm leaving the US? How big is IAD airport? and are there different terminals for domestic and international flights? If so, how long would it take to walk between them? Is there a way to "hide" a normal windowed application in Windows?  I'm looking for something that removes it from the taskbar and possibly puts an icon in the system tray instead. Consider the real-valued function  $f(x)=x^r$ where $r$ is a real number.  (1) For what values of $x$ and $r$, is this function differentiable?  (2) How do you prove the power rule, when $f(x)$ is differentiable?  It would be nice if the proof is accessible to a 12th grade student.  EDIT: Perhaps, I have not been very clear about my question.  I am not satisfied with the "textbook proofs" I have seen.  Please established the existence (of the derivative) first before proving the power rule.  That is, please consider first question first.  This is the reason why I call the question a mathematical engineering question.  (If we can we bring high level math down to Grade 12 level, without loosing precision, then I call it good mathematical engineering.) Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue. I can't find the missing link between singularity and zero eigenvalues as is stated in the following proposition:  A matrix $A$ is singular if and only if $0$ is an eigenvalue.  Could anyone shed some light? I'm asked to used induction to prove Bernoulli's Inequality: If $1+x&gt;0$, then $(1+x)^n\geq 1+nx$ for all $n\in\mathbb{N}$. This what I have so far:  Let $n=1$. Then $1+x\geq 1+x$. This is true. Now assume that the proposed inequality holds for some arbitrary $k$, namely that $$1+x&gt;0\implies (1+x)^k\geq 1+kx,~\forall~k\in\mathbb{N}\setminus\{1\}$$ is true. We want to show that the proposed inequality holds for $k+1$. Thus multiplication of $(1+x)$ on each side of the above inequality produces the following result: $$(1+x)(1+x)^k\geq (1+kx)(1+x)\implies (1+x)^{k+1}\geq 1+x+kx+kx^2\cdots\cdots\cdots$$  I'm not sure where to go from here. Small caps font warning in beamer using biblatex Consider the following MWE  \documentclass{beamer} \usepackage{silence} \WarningFilter{biblatex}{Patching footnotes failed}  \usepackage{lmodern} \usepackage[T1]{fontenc}  \usepackage[style=authoryear-comp,backend=biber]{biblatex} \addbibresource{biblatex-examples.bib}  \begin{document} \begin{frame}   \fullcite{sarfraz} \end{frame} \end{document}   This generates the warning:  LaTeX Font Warning: Font shape `T1/lmss/m/sc' in size &lt;10.95&gt; not available (Font)              Font shape `T1/lmr/m/sc' tried instead on input line 28.   Is there a way to avoid the warning without using the silence package? In Volo's Guide it is suggested that a curse could transform someone into a race of 'monstrous origin' (p. 118). Does this apply to the Bestow Curse spell specifically? Note: this is a  (my apologies).  In film / lore, such magic does , ,   - or even  transformative curses.  Points &amp; Concerns:   this is within guidelines for a 'reasonable' curse, i.e. less harm than the listed set Bestow Curse writeup encourages DM-homebrewing &amp;/or interpretation. Great role-play possibility / RAI (hence most myths, fairy tales, cartoons, legends, etc) this could be subject to abuse, temptation to bestow a 'curse' as a blessing / boon one could also change: age, size, weight &amp;/or gender (all great curse ideas... but RAW-legal?)   Summation:  What are the limits of the 3rd lvl / Necromatic Bestow Curse spell for transformation? How can I recover my account? I tried to log into Minecraft today to find that my password isn't working. I tried to change it, but I can't login to my email because I forgot the answer to my security question. I tried changing the email to a different one, but that didn't work for some reason (it kept saying "invalid email"). I don't have my transation ID because I forgot which credit card I used.  Does this mean that I have to buy a new Minecraft account? geometry package - paperwidth and paperheight aren't accurate recognize this simple example:  \documentclass[]{article} \usepackage[paperwidth=612.0pt, paperheight=792.0pt]{geometry}  \begin{document} Hello World \end{document}   I compiled it with pdflatex. Additionally I wrote this small Java-Programm (using the iText library):  PdfReader reader = new PdfReader("example.pdf"); Rectangle psize = reader.getPageSize(1); System.out.println(psize.getHeight()); System.out.println(psize.getWidth());   The result:  Height: 789.041 Width: 609.714   Why is the paperwidth and paperheight different to the tex? Not enough space in /var/cache/apt/archives/