I found this:     Fear is an essential attribute of human nature. It plays a crucial role in human survival.   But we cannot use:     Fear is an essential attribute of human nature. It plays a crucial role in human's survival.   Why?
I am firmly convinced he is innocent and his accusation is the result of the police conspiracy.     I am firmly convinced he is innocent and his accusation is the result of the police's conspiracy.    Which sentence do you think is a better choice?
For what natural numbers is $n^3 < 2^n$? Prove by induction Problem  For what natural numbers is $n^3 &lt; 2^n$?  Attempt @ Solution   For $n=1$, $1 &lt; 2$ Suppose $n^3 &lt; 2^n$ for some $n = k \ge 1$ It looks like the inequality is true for $n = 0$, $n = 1$ and $n\ge10$ But, how can I prove this through induction? Does the Sun produce audible sound? Flight Search from anywhere to a specific destination Many flight search engines allow you to pick a departure airport and search for flights to anywhere. E.g.  gives you a nice map with prices next to destinations for a set of dates and an origin you selected. We covered this question widely in  here on our site.  I want to have the reverse, i.e. I know my dates and my destination (for a one-way flight) and I want to know from where it is cheapest to fly there. Is there any flight search engine out there to achieve this?  Google flights does not do this, they pre-compile the "from"-field if I try to leave it empty. I know I could use  with a wide range of departure airports but that does not give me low-cost carriers and I do not trust the matrix results for such a wide range of parameters anymore.  Edit: It has been asked in comments why I would want such a feature. Well currently I'm planning my summer vacation and I would like to spend one week traveling around basically anywhere in that area before I have to go to a specific location at a specific time. One of the main price and convenience factors for me is that final flight so I would like to optimize it first. I'm sure I'm not the only one with that kind of constraints. What is the integral of $\int e^x\,\sin x\,\,dx$? I'm trying to solve the integral of $\left(\int e^x\,\sin x\,\,dx\right)$ (My solution):  $\int e^x\sin\left(x\right)\,\,dx=$  $\int \sin\left(x\right) \,e^x\,\,dx=$  $\left(\sin(x)\,\int e^x\right)-\left(\int\sin^{'}(x)\,\left(\int e^x\right)\right)$  $\left(\sin(x)\,e^x\right)-\left(\int\cos(x)\,e^x\right)$  $\left(\sin(x)\,e^x\right)-\left(\cos(x)\,e^x-\left(\int-\sin\left(x\right)\,e^x\right)\right)$  $\left(\sin(x)\,e^x\right)-\left(\cos(x)\,e^x-\left(-\sin\left(x\right)\,e^x-\int-\cos\left(x\right)\,e^x\right)\right)$  I don't know how to complete because the solution gonna be very complicated. How to fix "sudo: unable to open ... Read-only file system"? The title might not be as descriptive as I would like it to be but couldn't come up with a better one.  My server's file system went into Read-only. And I don't understand why it does so and how to solve it.  I can SSH into the server and when trying to start apache2 for example I get the following :  username@srv1:~$ sudo service apache2 start [sudo] password for username: sudo: unable to open /var/lib/sudo/username/1: Read-only file system  * Starting web server apache2                                                                                                                                                                                                               (30)Read-only file system: apache2: could not open error log file /var/log/apache2/error.log. Unable to open logs Action 'start' failed. The Apache error log may have more information.   When I try restarting the server I get :  username@srv1:~$ sudo shutdown -r now [sudo] password for username: sudo: unable to open /var/lib/sudo/username/1: Read-only file system   Once I restart it manually it just start up without any warning or message saying something is wrong.  I hope somebody could point me into the right direction to resolve this issue. How to make a good glow effect around a sun? Every irreducible polynomial $f$ over a perfect field $F$ is separable.   Can you check my proof? Assume that $f$ is irreducible but inseparable. So we have $f=\sum_i h_ix^i$ and $f^p=\sum_i h_i^px^{ip}$. Now I use Frobenius mapping $\phi (f)=f^p=(\sum_i h_ix^i)^p=\sum_i h_i^px^{ip}$ so it is reducible. Contradiction. Should I also show for char(F)=0? The Medibuntu Project has come to an end - what do I do now? If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable Does "She had a brother" mean that her brother is dead? My Friend has sent me this riddle to solve:     "If you solve this, then you are a genius. Mr.Smith has 4   daughters🙍‍♀🙍‍♀🙍‍♀🙍‍♀ and each daughter had a brother.  How many   children does Mr. Smith have now?"   He said the answer is not 5, but 4 only as in the riddle it is mentioned as each daughter had a brother. So their only brother is dead.     Is he right? I try to add an item to my sharepoint list from a custom web part. Is there any mistake in my code?  [WebMethod]         public static string AjouterDemande()         {             SPList ListeDemandeConge = SPContext.Current.Site.RootWeb.Lists["DEMANDE CONGÉ"];             SPListItem ListItem = ListeDemandeConge.Items.Add();             ListItem["CODE"] = code;             ListItem["DEMANDEUR"] = Utilisateur.LoginName;             ListItem["DATE DEMANDE"] = DateTime.Today.Date;             ListItem["DATE FIN"] = EndDateD;             ListItem["DATE DEPART"] = StartDateD;             ListItem["DUREE"] = int.Parse(DayCount);             ListItem["PREMIER RESPONSABLE"] = Employe.FirstSuperior.LoginName;             ListItem["DEUXIEME RESPONSABLE"] = Employe.SecondSuperior.LoginName;             ListItem["PRESENCE PRES"] = Boolean.Parse(FirstRespPresent);             ListItem["SOLDE CONGE"] = Conge.SoldeAnneeConge;             ListItem["MOIS"] = int.Parse(StartDateTab[1]);             ListItem["ANNEE"] = int.Parse(StartDateTab[0]);             ListItem["JOURS APPROUVEES"] = 0;             ListItem.Update();             ListeDemandeConge.Update();             return "true";          }   When I use F10 to process debugging step by step and get to my listitem.update(), it went out without giving any error. Changing the homepage Is it possible to change the Home page so it's not a blog, but a page? And also is it possible to change the name of the homepage?  If yes, how is this done?  Thanks, Richard Prove Lipschitz function $f$ with constant $K$ is integrable on $[0, 1].$ We suppose that $f : [0, 1] \rightarrow \mathbb{R}$ is a Lipschitz function with constant $K$. We want to show that $f$ is integrable on $[0, 1].$  I've been trying to use the Darboux criterion of integrability by trying to show that, for $\epsilon &gt; 0$, $$S^*(f,P) - S_*(f, P) &lt; \epsilon,$$ where $S^*(f, P)$ and $S_*(f, P)$ are the Upper and Lower Riemann Sums, respectively.  This is what I have so far: $$\sum_{i=1}^n M_i (x_i - x_{i-1})- \sum_{i=1}^n m_i (x_i - x_{i-1}) = \sum_{i=1}^n (M_i - m_i) (x_i - x_{i-1})$$ $$\le \sum_{i=1}^n K (x_i - x_{i-1}).$$ because $|f(x) - f(u)| \le K|x-u| \le K |1|$, since $x\in [0, 1]$. Then, $$\sum_{i=1}^n K (x_i - x_{i-1}) = K.$$ However, this is only a single upper bound, not an arbitrary $\epsilon.$ Can I get some pointers about how to proceed? Thanks! Why didn't Isildur's Heir come forward sooner? Natural Deduction - How to define literals? I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints? Render an InputText based on Selected Option In my VF page I have an apex:selectList with a List of Vendors (e.g. Alcatel,Cisco ec..), the last option is "Other".   When the user select "Other" an apex:inputText should be rendered  where he can writes the Vendor. I'm not able to render the inputText Field   My VF page:  &lt;apex:outputPanel id="vendor2"&gt; &lt;p&gt;&lt;b&gt; Vendor: &lt;/b&gt;&lt;/p&gt; &lt;apex:selectList value="{!vendor}" multiselect="False" size="1"&gt;     &lt;apex:actionSupport event="onchange" action="{!specifyVendor}" rerender="otherPanel"/&gt;     &lt;apex:selectOptions value="{!vendors}"/&gt; &lt;/apex:selectList&gt;&lt;p/&gt; &lt;/apex:outputPanel&gt; &lt;br/&gt; &lt;apex:outputPanel id="otherPanel"&gt;     &lt;apex:inputText value="{!otherVendor}" rendered="{!vendor=='Other'}"&gt; Other: &lt;/apex:inputText&gt; &lt;/apex:outputPanel&gt;     &lt;br/&gt;&lt;br/&gt;    The custom controller:      public with sharing class ExcelPageController {          public String vendor {get; set;}//Vendor Name         public String otherVendor {get; set;}//Vendor Name          public List&lt;SelectOption&gt; getVendors(){             System.debug('getVendors');                 List&lt;SelectOption&gt; options = new List&lt;SelectOption&gt;();             options.add(new SelectOption('Cisco','Cisco'));             options.add(new SelectOption('Alcatel','Alcatel'));             options.add(new SelectOption('Tibco','Tibco'));             options.add(new SelectOption('Other','Other'));             return options;         }     public PageReference specifyVendor(){         System.debug(vendor);         return null;     } } If $\sum_{n=1}^{\infty} a_n$ converges, then so does $\sum_{n=1}^{\infty} a_n^{\frac{n}{n+1}}$ Given a positive sequence $(a_n)$. Prove that if $\displaystyle \sum_{n=1}^{\infty} a_n$ converges, then so does $\displaystyle \sum_{n=1}^{\infty} a_n^{\frac{n}{n+1}}$.   I tried to use the root test, and I was stuck with the case $\lim \sup \sqrt[n]{a_n}=1$. Maybe we need some trick here.  Thanks so much. How to prove floor identities? UIDatePicker show only month and day I'd like to have a UIDatePicker where the user can pick a month and a day but not the year. I'm aware that leap years have an extra day, so for simplicity, let's throw that day away.  Is there any way to remove the year column or have 2 reels with month/day that act like the UIDatePicker (grey out days that don't exist in the selected month)? Why the "service --status-all | grep mysql" get many unrelated result?