Centering two elements horizontally? I have this problem where I want to line up two elements (a &lt;p&gt; and a &lt;button&gt;) but I can't seem to find a way of lining them up; I have tried using padding, margin, flex and even grid design, but nothing seems to work. Here is an image showcasing the problem:  And here is a code snippet of my latest attempt:   .line p {   display: inline-block;   margin: 0;   padding-top: 10px;   padding-bottom: 10px;   font-family: 'Oswald', sans-serif;   font-size: 20px;   width: 100%;   border-bottom: lightgray solid 1px; }  .activeLine {   color: #38B938;   background-color: white; }  .buttonsActive {   background-color: inherit;   border: 1.5px solid #38B938;   color: #38B938;   padding: 8px 15px;   text-align: center;   text-decoration: none;   display: inline-block;   font-size: 16px;   margin: 4px 2px;   cursor: pointer;   font-family: 'Oswald', sans-serif;   border-radius: 50%; }  .inactiveLine {   background-color: white; }  .inactiveLine {             background-color: white;         }          .buttonsA {             background-color: inherit;             color: black;             padding: 8px 15px;             text-align: center;             text-decoration: none;             display: inline-block;             font-size: 16px;             margin: 4px 2px;             cursor: pointer;             font-family: 'Oswald', sans-serif;             border-radius: 50%;             float: right;             margin-right: 10px;          }          .buttonsA:hover {             color: #38B938;             transition: linear 0.5s;         }          .buttonsA:first-child {             margin-left: 10px;             float:left;             border: 1.5px solid black;         }          .buttonsA:first-child:hover {             color: #38B938;             border: 1.5px solid #38B938;             transition: linear 0.5s;         }          .buttonsActive:first-child {             margin-left: 10px;             float:left;         } &lt;div class="voiceGrid"&gt;   &lt;div class="titleVoiceBanner"&gt;     &lt;h2 class="textVoiceTitle"&gt;Problem for  &lt;/h2&gt;     &lt;h3 class="textVoiceSubtlt"&gt;Stack Overflow&lt;/h3&gt;   &lt;/div&gt;      &lt;div&gt;     &lt;audio id="player1"&gt;        &lt;source type="audio/mpeg"&gt;     &lt;/audio&gt;     &lt;div class="line inactiveLine" id="line1"&gt;       &lt;p&gt;         &lt;button id="buttonPlay" class="buttonsA"&gt;▶&lt;/i&gt;&lt;/button&gt;                    Loc 1                &lt;/p&gt;      &lt;/div&gt;   &lt;/div&gt;   &lt;/div&gt;
How can I vertically align elements in a div? I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers? &lt;div id=&quot;header&quot;&gt;   &lt;img src=&quot;..&quot; &gt;&lt;/img&gt;   &lt;h1&gt;testing...&lt;/h1&gt;   &lt;img src=&quot;...&quot;&gt;&lt;/img&gt; &lt;/div&gt;
How should you deal with (deliberate) selective deafness? Let $A$ be a $m \times n$ matrix with entries from some field $F$. Define the determinant rank of $A$ to be the largest possible size of a nonzero minor, i.e. the size of the largest invertible square submatrix of $A$. It is true that the determinant rank is equal to the rank of a matrix, which we define to be the dimension of the row/column space.  It's not difficult to see that $\text{rank} \geq \text{determinant rank}$. If some submatrix of $A$ is invertible, then its columns/rows are linearly indepedent, which implies that the corresponding rows/columns of $A$ are also linearly indepedent.  Is there a nice proof for the converse? How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? Bernhard Elsner, alias MathOMan, posted this exercise in plane Geometry,  on January $29$th, $2010.$  "Let $\mathcal{C}$ be a circle, $A,B$ two distinct points on $\mathcal{C}$ and $M$ be the midpoint of the chord $[AB]$. Take two other chords,$[PQ]$ and $[SR]$, that pass through $M$. Let $C$ (resp. $D$) be the intersection of $[AB]$ with $[PS]$ (resp. $[RQ]$). Prove that $M$ is the midpoint of the chord $[CD]$."    To prove it I've written the following (failed) argument, in the  of this post (translation of mine):    The figure is symmetric with respect to $M$: $\overline{AM}=\overline{MB}$, $\overline{PM}=\overline{MU}$, $\overline{RM}=\overline{MW}$, $\overline{QM}=\overline{MV}$, $\overline{QR}=\overline{VW}$, $\overline{SM}=\overline{MT}$. From $\dfrac{\overline{SC}}{\overline{DT}}=\dfrac{\overline{CM}}{\overline{MD}}=1$ follows that $\overline{CM}=\overline{MD}$.  Here is an extract of the author's reply (translation of mine):   "It is not clear that  $\overline{QM}=\overline{MV}$. Is the point $V$ on the line $(QM)$ defined by this equality or is $V$ defined as the intersection point of the lines $(QM)$ and $(WC)$? Why are both definitions to give the same point?  Let $C^{\prime }$ be the intersection of $(SP)$ and $(VW)$, and $D^{\prime }$ the intersection of $(TU)$ and $(QR)$. (...)  One still has to show that $C^{\prime }=C$ and $D^{\prime }=D$."   I have agreed with these objections.  Until now no proof has been posted. The author considers that the "proof is not quite simple".  Q. What is the theorem this exercise refers to? Or how does one prove it? How does finder sort folders when they contain digits and characters? Arrays, linked lists and other data structures in cmd.exe (batch) script Proof explanation $A\setminus B = A \setminus B \cap A$ $A\setminus B = A \setminus B \cap A$  Proof $A\setminus B \subseteq A \setminus B \cap A$:  $x\in A\setminus B \to x\in A \land x \notin B$  $x\in A \land (x \notin B \color{red}{\lor x\notin A})$  $x \in A \land (x\notin B \cap A)$  $x \in A\setminus B\cap A$  Proof $A \setminus B \cap A \subseteq A\setminus B$:  $x \in A \setminus B \cap A \to x\in A \land x\notin B \cap A$  $x \in A \land (x\notin B \color{red}{\lor x\notin A})$  $x \in A \land x \notin B$  $x \in A \setminus B $  Therefore $A\setminus B = A \setminus B \cap A$  I am confused how the stuff in the red is formed. Can we add an or statement to anything and ignore if its true or not if the first part of the or is true? How do we know an $ \aleph_1 $ exists at all? I have two questions, actually. The first is as the title says: how do we know there exists an infinite cardinal such that there exists no other cardinals between it and $ \aleph_0 $? (We would have to assume or derive the existence of such an object before we label it something like $ \aleph_1 $.)  My second question is, can we say for certain if there's any limit to the number of cardinals existing between $ \aleph_0 $ and continuum (i.e. $ 2^{\aleph_0} $)? I mean, how could we know that there&#39;s not an infinite number of cardinals between the two - perhaps even more than $ \aleph_0 $? Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$. I don't know how to solve this problem. I tried to write out the sum of products in the definition of products of ideals, but that doesn't seem to lead anywhere. I accidentally installed some USB drivers to my Windows 7 system, they were the wrong ones and now my keyboard and mouse won't work. A system restore would get rid of them, but obviously I can't control my computer to make that happen.  Keyboard and mouse still work before windows has loaded, in the BIOS and boot system, so can I do anything from there? I've already tried booting into another OS, accessing my windows filesystem and deleting the Program Files entry, but it didnt work so they must go deeper than that. Or could i launch it from a remote machine? I've got some VNC server insalled so if i could get that running that could work. SQLiteException while inserting values in the database in Android From Geneva airport to Lausanne station On September 4, I will be arriving in Geneva by airplane at approximately 11 AM. After that, I need to go to Lausanne. I have two questions:   Do I need to buy a train ticket online, or can I buy it directly at the station without any problems? (Problems such as: the trains are always full, it's not permitted to buy a ticket etc.) Moreover, are the tickets only for a specific train or it is like "you can board any train from Geneve to Lausanne with this ticket"? How do I get from the airport to the Geneva train station (as low a budget as possible, I guess walking is not an option though), and how much does it cost?   I'd appreciate answers from people who have been there, but if you're able to find an exhaustive link from any website that's okay too. Acknowledgements outside of document environment How do I add an acknowledgements section (maybe not specifically \section) outside of (before) my document environment?  in my .cls, there is  \def\@acknowledge{} ... \def\acknowledge#1{\booltrue{@ack} \gdef\@acknowledge{#1}} ... \def\ackpage{ \chapter*{Acknowledgments} \@acknowledge \newpage }   but it seems that I find problems when I put newlines in the  \acknowledge{folks in here}  (see  ) How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$? How to solve this limit without using L'Hospital rule?  $$\lim_{x \rightarrow 0}{\frac{(1+x)^a-1}{x}}$$ Did the Big Bang happen at a point? TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen? Is there a way to detect if a browser window is not currently active? What if the Earth stops in its orbit and instead falls straight towards the Sun? The Earth orbits around the Sun because it has angular momentum. If we stopped the Earth in orbit and then let it fall straight towards the Sun, how long would it take to reach the Sun in seconds?  Details and assumptions  The mass of the sun is 2*10^30 Kg. The mass of the earth is 6*10^24 Kg. The earth is 149,600,000 Km from the Sun. You may treat the Earth and Sun as point masses. What is a simple example of a limit in the real world? This morning, I read Wikipedia's informal definition of a limit:     Informally, a function f assigns an output $f(x)$ to every input $x$. The   function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever   $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$   as $x$ moves closer and closer to $p$.   To me that sounds like something that might be better described as a 'target'.  If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).   So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.   What is a simple example of a limit in the real world?  Thank you  -Hal. Properties of $y$ if $\frac{d^2y}{dx^2}+xy=0$, $x \in [a,b],$ and $y(a)=y(b)=0.$ Let $y$ be a nontrivial solution of the boundary value problem  $$\frac{d^2y}{dx^2}+xy=0,\ x \in [a,b]$$  $$y(a)=y(b)=0$$ Then:   $b&gt;0$ $y$ is monotone in $(a,0)$ if $a&lt;0&lt;b$. $y'(a)=0$. $y$ has infinitely many zeros in $[a,b]$   I have no idea how to solve it and which options is/ are correct. please help me. How to blacklist kernel modules? What is the relation between linear purity and von Neumann entropy of a state? Given a density matrix $\rho$, its linear purity is $\mathrm{Tr} \rho^2$, its von Neumann entropy is $-\mathrm{Tr} \rho \log \rho$. Knowing one how do I calculate the other?  Edit:   My thought is that the linear purity and the von Neumann entropy are a parallel set of benchmarks for mixedness. Their inter-conversion should be like unit conversion.  See it this way, as a state goes from a pure state to a maximally mixed state, $\mathrm{Tr} \rho^2$ goes from $1$ to $0$, and $-\mathrm{Tr} \rho \log \rho$ goes from $0$ to $\log d$, like two rulers. A point on one should correspond to a point on the other.