Why there is this white space above my containers,     * {     padding: 0;     margin: 0; }  .hamburger {     position: relative;     background: #eee; }  .bar {     background: orange;     position: relative;     margin-top: 150px;  } &lt;div class="hamburger" id="hamburger-1"&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt; &lt;/div&gt;  &lt;div class="hamburger" id="hamburger-2"&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt;    &lt;div class="bar"&gt;hi&lt;/div&gt; &lt;/div&gt;  &lt;div  class="hamburger" id="hamburger-3"&gt;     &lt;div class="bar"&gt;hi&lt;/div&gt;     &lt;div class="bar"&gt;hi&lt;/div&gt;     &lt;div class="bar"&gt;hi&lt;/div&gt; &lt;/div&gt;     When i add margin-top: 150px for .bar elements seems i get white space above the whole container not inside it, this is unexplained to me!!  Can anyone explain this bahavior??
So essentially does margin collapsing occur when you don't set any margin or padding or border to a given div element?
#!/bin/bash - no such file or directory I've created a bash script but when I try to execute it, I get   #!/bin/bash no such file or directory   I need to run the command: bash script.sh for it to work.  How can I fix this? How do you configure email notifications in Cognito Forms? The most efficient way to implement an integer based power function pow(int, int) How do I set a Boolean field with "yes" and "no" values? Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$ Where $a,b$ and $c$ are positive real numbers.  So far I have shown that $$a^2+b^2+c^2 \ge ab+bc+ac$$ and that $$a^2+b^2+c^2 \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$$ but I am at a loss what to do next... I have tried adding various forms of the two inequalities but always end up with something extra on the side of $ab+bc+ac$. Any help appreciated! How did we 'discover' dark matter? I'm an astrophysics student and I've been researching this topic and there is one point that keeps eluding me.  How did the scientific community realize that there had to be  in the Universe? Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$ This is being asked in an effort to cut down on duplicates, see here: , and here: .    What methods can be used to evaluate the limit $$\lim_{x\rightarrow\infty} \sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x.$$  In other words, if I am given a polynomial $P(x)=x^n + a_{n-1}x^{n-1} +\cdots +a_1 x+ a_0$, how would I find $$\lim_{x\rightarrow\infty} P(x)^{1/n}-x.$$  For example, how would I evaluate limits such as $$\lim_{x\rightarrow\infty} \sqrt{x^2 +x+1}-x$$ or $$\lim_{x\rightarrow\infty} \sqrt[5]{x^5 +x^3 +99x+101}-x.$$ How to compare objects by multiple fields Assume you have some objects which have several fields they can be compared by:  public class Person {      private String firstName;     private String lastName;     private String age;      /* Constructors */      /* Methods */  }   So in this example, when you ask if:  a.compareTo(b) &gt; 0   you might be asking if a's last name comes before b's, or if a is older than b, etc...  What is the cleanest way to enable multiple comparison between these kinds of objects without adding unnecessary clutter or overhead?   java.lang.Comparable interface allows comparison by one field only Adding numerous compare methods (i.e. compareByFirstName(), compareByAge(), etc...) is cluttered in my opinion.   So what is the best way to go about this? So I was thinking... If heat I feel is just lots of particles going wild and transferring their energy to other bodies, why am I not burned by the wind?  When I thought about it more I figured out that wind usually carries some humidity, and since particles of liquid are moving same speed as the wind, they are basically static relative to each other, so no energy is transferred between them (wind and water particles). And if that water sticks to my skin and wind blows, it'll evaporate thus taking energy from my skin and make me feel cold.  Thing is, I don't think that's really the case but even if it is, if I somehow dry out the wind, will it burn me if it's strong enough? And winds can reach some pretty high velocities (though I must admit I'm not sure if they are comparable to movement of atoms in warm bodies etc...).  So. Bottom line. Can I be burned by wind in some perfect scenario? I want to draw a table and i used the following code  \begin{table}[htbp]  \centering \caption{Ship simulator required inputs} \begin{tabular}{|c|c|} \hline L_{PP},  L_{WL}, L_{OS}, B, T, T_{a}, T_{f}, C_{B}, D_{P}, `\\` Bulbous bow, Number of bosses, brackets, thrusters. &amp; ship particulars `\\` \hline Required speed or propeller rpm, ship course angle &amp; Mission data \\ \hline BN, weather angle, water temperature &amp; Environment \\  \hline \end{tabular}% \label{inputs}% \end{table}%`   the result of this is as shown in figure    How can i complete the right border of the table ??? I used \\ to break the line of first row "Pupil" or "Student", what is the correct use? What do we lose passing from the reals to the complex numbers? As normed division algebras, when we go from the complex numbers to the quaternions, we lose commutativity. Moving on to the octonions, we lose associativity. Is there some analogous property that we lose moving from the reals to the complex numbers? Solve Euler Project #9 only mathematically - Pythagorean triplet The "Euler Project" problem 9 () asks to solve:  $a^2$ + $b^2$ = $c^2$ a + b + c = 1000  I find answers solving it with brute-force and programmatically, but is there a way to solve the problem ONLY mathematically? Can someone help, please?  Problem as explained in Project Euler website:  A Pythagorean triplet is a set of three natural numbers, a &lt; b &lt; c, for which,  a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 52.  There exists exactly one Pythagorean triplet for which a + b + c = 1000.  Find the product abc. $\zeta_{15}$ is $15$th primitive $n$th root of unity.   Question: Find the structure of the group $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$  I know that if $p$ is prime then $G=Gal(\mathbb{Q}(\zeta_{p})/\mathbb{Q})=\mathbb{Z_{p}}^*$ but when $p$ is not prime, I am not show how to solve this if not prime.  Does my required group have any relation to some cyclic group $\mathbb{Z_n}$, i.e. abelian  Would really appreciate your guidance as I have not got my head around these concepts of cyclotomic fields and Galois structure. Thanks Representing network flows? For a project I'm working on, I need to represent network flows over 1,000 zones with directionality.    Any suggestions on displaying the information in a nice and non overwhelming way?  Any examples on displaying network flows in heavy urban areas? Color suggestions and thickness schemes? any "not to dos" when representing network flows? Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$ I have this proposition to prove: The equation $x^2 = -1$ has no solution in $\mathbb Z$. I was told that this is an opportunity for a proof by contradiction. I have already proven that for $m \in\mathbb Z$, if $m \ne 0$ then $m^2 \in\mathbb N$. I have also proven that 1 is a natural number (hence, -1 isn't one).  Here is my strategy: assume that there is a solution. Hence $x^2$ has 3 options: \begin{align*} x^2 \in\mathbb N\\ -(x^2) \in\mathbb N\\ x^2 = 0 \end{align*}  Option 1 is not possible because -1 is not a natural number. Option 2 doesn't make sense because         -$\mathbb N \in \mathbb N$ and option 3 doesn't make sense either because $0 \ne -1$. What do you think? Thank you!    Here is a simpler strategy based on the comments below.  Proof: Assume that $x^2 = -1$ has a solution in $\mathbb Z$, then $x^2$ will either be $0$ or $\in\mathbb N$. However, $-1 \notin\mathbb N$ and $-1 \ne 0$. Hence, there is a contradiction. Here is how I have proven that $-1 \notin\mathbb N$: Let $m \in\mathbb N$. Hence:  \begin{align*} -m \notin\mathbb N\\ (-1)m \notin\mathbb N \end{align*}  If $-1 \in\mathbb N$, the product of $-1$ and $m$ should $\in\mathbb N$, which is not the case here. Hence, $-1 \notin\mathbb N$. Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. Why is $ \overline{e^z} = e^\overline{z} $? How can you conjugate an entire function? $ \overline{exp(z)} $ I need an equivalent.  I thought this is only possible with complex numbers.   What is the proof for $ \overline{e^z} = e^\overline{z} $ ? (Please don't involve a power series here.) How can I get barcode-scan information into my photo metadata, onsite, untethered? I need a DSLR camera with a barcode scanner for on-site tours photography, which means it needs to be untethered! The image would have to contain the barcode scanned information in the image metadata or in the name itself.  I've seen solutions like, Foolography and a $2600 Canon Studio Edition launched in 2010. But I'm not sure of either those products!  So I'm asking the gurus here how I can get this working, which camera would I need and any accessory necessary?  I'm trying to recreate something like I saw the on-site volume photographers do in Disney's parks.