What does the expression "to stick the finger high in the air" mean? It is used in the text about politics.
Could anyone give me an explanation of the meaning of "get one's finger in the air" and the usage of it?
I want to prove the definition of limit of a function from definition (1) to definition (2).  (1) A function $f(x)$ is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for every sequence $\{x_n\}$ with limit $x^*$, the limit $\lim_{n-&gt;\infty}f(x_n)$ exists and is equal to $f^*$. (2) A function is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for each $\epsilon &gt;0$, there exists a $\delta_\epsilon &gt;0$ such that $|f(x)-f^*| &lt;\epsilon \forall |x^*-x|&lt;\delta_\epsilon$  I am confused about the steps. Suppose I am given an $\epsilon &gt; 0$ and $x^*$. I have to show the existence of a $\delta_\epsilon &gt;0$ such that for all $x$ satisfying  $|x^*-x|&lt;\delta_\epsilon$ I can construct a sequence $x_n$ which converges to $x^*$ and $x_n=x$ for some $n \geq N$. Then I can say that $f(x_n)-f^*=f(x)-f^* &lt; \epsilon$. I think I may have made some mistake about the steps.  My main confusion is the following : Suppose I choose $\delta_\epsilon=\epsilon$. Then if a sequence $\{x_n\}$ converges to $x^*$ then $x_n=x$ (where $x$ satisfies $|x-x^*|&lt;\epsilon$) for some $n\geq N$. Now, $\lim_{n-&gt;\infty}f(x_n)$ exists implies there exists an $M$ such that $\forall n\geq M$, $f(x_n)-f^* &lt;\epsilon$. Now, I need to show that for some $n \geq M$ indeed $x_n=x$. How do I show that ? This $M$ and $N$ are different. When did 5 foot squares become standard in D&D? I installed Ubuntu (twice actually) onto the same drive. I wanted to 'try again' since one of them didn't install correctly and the other installed differently, but it worked.   I was getting frustrated with the GRUB menu because it was really sloppy (There were two Windows options - one with the Windows bootloader to go into Ubuntu, and two different versions of Ubuntu from the first install for some reason and memtest, etc.).  In my attempts at getting rid Ubuntu to do a fresh installation, I went ahead and deleted the partitions that weren't swap or main via Windows 7. As I said, I am a noob.  Now, even though I though I completely got rid of Ubuntu, including the GRUB menu, when I boot my PC I am brought directly to GRUB Rescue. And from what I've found from other forums, GRUB rescue isn't even completely functional for me (it doesn't recognize any commands that it should support besides ls. It also returns unknown filesystem for any partition I try to view or boot.)  Is there any way that I can boot straight into Windows? I fear I may have gone about deleting those partitions in the wrong way. If so, what are my options? How to cut holes in an object using another object? I'm trying to model a M16 but I have a problem with cutting the holes on top of the handguard of the weapon.     As you can see in the picture above, I have tried to cut holes into the handguard (The marked mesh in edit mode) with the object above it (The multiple cylinder one). But I simply can't. I have tried the Boolean modifier but the handguard just disappears and doesn't make any holes. Same with the Knife Project thing. Nothing works, it won't make a hole in it. I also installed the BoolTool 0.2 but that didn't work either...The multiple cylinder object goes invisible and doesn't make any cuts.    In the picture above you can see how I want the cuts to be made. I want the holes of the multiple cylinder object to be there on the handguard when I take it away. Nothing works. The 3 methods I tried with worked on other parts of this model but not on the handguard. It should be the handguards mesh's fault but I can do nothing about it. Is there any solution? I don't really know much about entropy but I learned recently that the entropy in the universe is constantly increasing and that perhaps someday we will reach maximum entropy and the universe will end in heat death. In order for this to be true there are two prerequisites:   Heat must constantly be created. There must be no way to destroy heat (at least no way that turns it into a more useful form of energy).   1 is certainly true. Every process creates some heat. When a person walks his/her feet hit the ground with kinetic energy and the friction creates heat.   But I don't see how 2 can be true. For one thing, heat never even leaves its place of origin (earth, another planet or a star). In order for heat to travel in requires air (or some other conductor/convector). Since there is no air in space there is also no heat. Heat leaves things only in the form of electromagnetic radiation (light) (in the case of earth, infrared).   So conversion from heat to light is certainly possible and is even found in nature. Now how do we get from light to other forms of energy? Well, photosynthesis. Solar panels. So this is possible too. If so, why will we ever run out of useful energy? Even if the rest of the universe does, can't we still reharness our own energy by converting the heat to light and light to other forms of energy?  Suppose the sun died (and leave aside the fact that it would first destroy earth with a supernova), can't we just put up a huge solar panel around earth to pick up all the infrared and convert it back to useful energy? Flying Turkish Airlines, what are credit card rules? I have return tickets flying out of SFO on Turkish airlines for the whole family. The credit card I used to book the tickets has since been replaced by the bank with a new card.   In order to board, can I present the new credit card (same name) at the checkin counter, or must I present the original credit card (which is no longer valid and has been discarded)?  By 'discarded' - I mean cut up and thrown away in trash. It was no longer valid, since it was replaced with a new card. So can I use the new card to travel on a booking that was made using the original card?    The new card has a new number; and the ticket was purchased through an agent. I was trying to do some of these questions to check my understanding about the topic, but I'm not sure if they're correct. Here are my answers.   1) Suppose $f$ is continuous on $[0,1]$. Must there be a nondegenerate closed subinterval $[a,b]$ of $[0,1]$ for which the restriction of $f$ to $[a,b]$ is of bounded variation?   No, because $f(x)$ might be a constant function. In this case, $f(x)$ will not be the difference of two increasing functions...and so will not be of bounded variation.  2) Let $f$ be the Dirichlet function, the characteristic function of the rationals in $[0,1]$. Is $f$ of bounded variation on $[0,1]$?   No, because we cannot express it as the difference of two increasing functions.  3) Let $f$ be a step function on $[a,b]$. Find a formula for its total variation.  If we partition $[a,b]$ in such a way that for each $[x_{i-1}, x_i]$ (which is part of the partition), $x_{i-1}$ and $x_i$ each correspond to the midpoint of a step. I know this is not a formal answer, but I'm just trying to check my understanding. Windows 10 upgrade led to grub rescue Equal simple field extensions? I have a question about simple field extensions.  For a field $F$, if $[F(a):F]$ is odd, then why is $F(a)=F(a^2)$? I am failing to add a heading for the appendix to the ToC with the correct page number:  \documentclass{scrbook} \begin{document} \tableofcontents \chapter{test} \appendix \addcontentsline{toc}{part}{\appendixname} \chapter{First Appendix} \end{document}     I also tried to use the \addappheadtotoc command from the  package, but that changes nothing (expect that it writes 'Appendices' instead).  I assume that the appendix package provides the solution, but I could not figure out how to use it. How do we prove that  $\operatorname{rank}(A) = \operatorname{rank}(AA^T) = \operatorname{rank}(A^TA)$ ?  Is it always true? Command Options on Command Line - Details and Functions? Do Thorncaster Sliver's triggered abilities go on the stack? I was guessing, since you actually target things instead of just dealing damage (similar to ), 's triggered abilities would actually go on the stack.  This came up in a separate game this past Friday when the Sliver deck attacked with two s, one , and two s while his opponent had a  as well as some 2/2.  The reason this even came up was because, if the triggers went on the stack, you could target things so they resolve in the following order:   Predatory Sliver targets Blood Artist, killing it. Predatory Sliver targets the 2/2, dealing one damage to it. Thorncaster Sliver targets the 2/2, killing it. and 5. Both Manaweft Slivers target the player, dealing one damage each to him. Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$ What would be the sum of the following series?  $$\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$$  Thanks Text in Ubuntu Software Center is unreadable When I do a search in the software center this is what the results look like.    I can only see the text if I select one of them.  I tried changing themes but that didn't fix it. How to use "fit" to frame the nodes and labels I'm using the fit TikZ library to fit a rectangle around two nodes which include labels. However, the rectangle is only fit around the actual nodes, not about their labels:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{fit}  \begin{document} \begin{tikzpicture}   \node [label=label1,draw] (node1) {Node1}; \node [label=label2,draw] (node2) at (4,2){Node2};  \node[fit=(node1)(node2), draw] {}; \end{tikzpicture} \end{document}     How to fit the rectangle also around the node labels? Not flying the first leg of the journey – Company cancels the second-leg ticket I've a friend that booked a round-trip journey. He booked A-to-B and B-to-A. Somehow he needed to be earlier at location B, so he took a train and did not take the flight from A to B.  When he went to the airport to take the "back home" flight (B-to-A), he was informed that his ticket was canceled because he did not take the A-to-B flight. They canceled the ticket and sold it to someone else.  Is this normal? The company said it was their right to do so, and he could not get the flight back. The company was Iberia. What's the difference between the server version and the desktop version? What is the best way to copy a folder and all subfolders and files using c# If friction acts on car all time, why is it not accelerating forever? In the first gear, slowly releasing my clutch i push the gas pedal to the maximum torque level, say at 2000 rpm. Now as the engine torque is acting on the wheel, friction helps the car to accelerate.   If i hold the gas pedal at that position, the torque should continuously act on the wheel and the car should increase speed forever. But in reality even if we put the gas pedal at the max.torque rpm range in first gear it speeds up to certain wheel rpm (say 500rpm) and it stays there only. Why?