I was writing an article and try to insert an image with a caption. So first I used the following codes,  \flashright \includegraphics[scale=0.25]{cantor.png}   which results in     Then I wanted to add a caption below the image, so I used the following codes  \begin{figure} \flushright \includegraphics[scale=0.25]{cantor.png} \caption{cantor set} \end{figure}   which gave me,    So my question is how can I fix this large gap and make the things look like the first image with the caption underneath the image?
How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference
Linux Equivalent of Windows Ctrl to show Mouse Pointer In Windows, it is possible to set pressing Ctrl to display the current location of the mouse pointer, as per .  Is there a way of setting a key or key combination to perform the same action in Ubuntu? Note, this is the opposite of turning this function off, as detailed at . Find $\lim_{x\to 1}\frac{p}{1-x^p}-\frac{q}{1-x^q}$ Find $\lim_{x\to 1}(\frac{p}{1-x^p}-\frac{q}{1-x^q})$    My attempt: I took LCM and applied lhospital but not getting the answer.Please help I forgot my username, how do I get it back? I have installed Ubuntu 12.04-64 bit on my Lenovo IdeaPad laptop, and the wired Ethernet (LAN) connection doesn't work.  Running the lspci -vv | grep Atheros command from the terminal shows me I have the AR8161 Gigabit Ethernet controller:  02:00.0 Ethernet controller: Atheros Communications Inc. AR8161 Gigabit Ethernet (rev 08)   This looks like a new product whose drivers are not built into Ubuntu.  How do I install drivers to get the AR8161 working? I'd like to show that the class of all limit ordinals, LIM, is cofinal in the class of all ordinals ON.  I thought that I could do this by contradiction and assume that it wasn't cofinal in ON. Then there is an $\alpha \in$ ON such that for all $\beta \in $ LIM: $\beta &lt; \alpha$, i.e. $\beta \in \alpha$ and hence LIM $\subset \alpha$.  This means that LIM is a set so we can consider $\bigcup$ LIM. Then we have $\beta &lt; \bigcup$ LIM for all $\beta \in$ LIM by definition of $\bigcup$ LIM. So LIM $\subseteq \bigcup$ LIM.   $\bigcup$ LIM is either a limit or a successor ordinal.  If it is a limit ordinal then $\bigcup$ LIM $\in$ LIM and by transitivity of ON, $\bigcup$ LIM $\subseteq$ LIM, so $LIM = \bigcup$ LIM in this case which would mean that $\bigcup$ LIM $\in$ LIM $= \bigcup$ LIM which would be a contradiction because sets cannot contain themselves. Hence $\bigcup$ LIM cannot be a limit ordinal.  If $\bigcup$ LIM is a successor ordinal then $\bigcup$ LIM = $\beta \cup \{&#160;\beta \}$ for some $\beta \in $ ON.  Now I'm not sure how to proceed from here. I'm also not sure about whether I'm on the right track with this proof because I think there should be a shorter way  to prove this.  Thanks for your help. show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ Show that $\displaystyle\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ for all $k,l, n\geq 0$ with $k+l \leq n.$  The $k+l\leq n$ part doesn't seem that important. The claim clearly holds for $n=0,$ and in that case $k$ and $l$ must both be zero. I think the claim can be shown by induction, but I'm not sure how to do so; I'm not sure how to use the inductive hypothesis to prove the inductive step. The sum on the LHS is not always an integer, so finding a combinatorial argument doesn't seem very feasible. For $n = 1,$ we can have $(k,l) = (0,0), (1,0), (0,1),$ and in each case the sum holds. Perhaps multiplying both sides by a number (idk ${n-l\choose k}$) might be useful? Factors for max CP at a particular trainer level? I was reading about the equipartition theorem and I got the following quotations from my books:  A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis down the length of the molecule doesn't count. - Daniel V. Schröder's Thermal Physics. A diatomic molecule can rotate like a top only about axes perpendicular to the line connecting the atoms but not about that line itself. - Resnick, Halliday, Walker s' Fundamentals of Physics.  Why is it so? Doesn't the rotation take place that way? What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod&lt;T&gt;() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod&lt;T&gt;()?         GenericMethod&lt;myType&gt;(); // This doesn't work          // What changes to call StaticMethod&lt;T&gt;()?         Sample.StaticMethod&lt;myType&gt;(); // This also doesn't work     }      public void GenericMethod&lt;T&gt;()     {         // ...     }      public static void StaticMethod&lt;T&gt;()     {         //...     } } Making adult decisions are/is really not fun.     What is the proper answer and why? My gut says "is" but I can't explain why. Showing that $e^z=z$ has infinitely many solutions One of our review problems for my complex analysis final is the following:     Show that $e^z=z$ has infinitely many solutions in $\mathbb{C}$.   I've seen a few solutions online, but none of them have used material that was covered in our introductory complex analysis course. Would anyone be able to provide a simple solution?  I'm trying to think of ways to invoke bounding in some way but I can't seem to come up with anything. What's the best way of replacing a plug or switch in a house with aluminum wiring? What form of the verb is used with compound subjects containing "or"? If $\left|z+\frac{2}{z}\right |=2$, then prove that max value of $|z|$ is $\sqrt 3 + 1$ (Corrected version) Then the expression will be  $$|z|+\frac{2}{|z|}\ge 2$$  Solving the quadratic inequality   $$|z|\ge1+i$$ and $$|z|\le1-i$$  I don’t know how to solve further. Please help  Thanks!   this is the corrected version of an identical question asked by me. I am sorry for the inconvenience caused Unused Business visa I got a 6 months business visa for the UK. But I can't use it.   My relative lives in the USA. In the future, I want to go there to meet with her.  Is there any problem getting a US visa after getting, but not using, a UK business visa? Convert a string to an enum in C# Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? Calculate expected values using logistic regression coefficients Quantum teleportation and no-communication theorem According to the Wikipedia article for the :     In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. This analogy is imprecise, because quantum entanglement suggests that perhaps a message could have been conveyed; the theorem replies 'no, this is not possible'.   According to the Jet Propulsion's recent article on quantum teleportation:   they can effect an entangled photon (B) with another photon (A) to change the state of the other entangled photon.  Doesn't this contradict what the no-communication theorem states ? Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$