Force change array key to continous numbering
How do you reindex an array in PHP but with indexes starting from 1?
Iteration over std::vector: unsigned vs signed index variable What is the correct way of iterating over a vector in C++?  Consider these two code fragments, this one works fine:  for (unsigned i=0; i &lt; polygon.size(); i++) {     sum += polygon[i]; }   and this one:  for (int i=0; i &lt; polygon.size(); i++) {     sum += polygon[i]; }   which generates warning: comparison between signed and unsigned integer expressions.  I'm new in the world of C++, so the unsigned variable looks a bit frightening to me and I know unsigned variables can be dangerous if not used correctly, so - is this correct? If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24. I have a hard time formulating proofs.  For this problem, I  can see that if $n$ is equal to $8,$ this statement is true.  $(\mathbb{Z}/8\mathbb{Z})^{\times}$ includes elements:  $1,3,5,7$, and all of these are roots of $1-x^2 \pmod 8.$  And obviously $8$ divides $24.$  But how do I prove this without depending on number calculations and only using theorems?  Help Please?  I need a step by step walk through of how to do this proof and what theorems would be appropriate to use. Why do statisticians discourage us from referring to results as "highly significant" when the $p$-value is well below the conventional $\alpha$-level of $0.05$?  Is it really wrong to trust a result that has 99.9% chance of not being a Type I error ($p=0.001$) more than a result that only gives you that chance at 99% ($p=0.01$)? I am designing gamecards in LaTeX  Everything is going pretty ok so far but when i try to insert the %-sign for a question about percentages my file keeps giving errors.  I tried putting the percentage between dollarsigns because i know just % will make it a 'remark' and that the dollarsign makes it 'mathematical data'.   Whats the reason for the error?   P.s. the error says: file ended while scanning use of \kaart. ...    Codesample:   {\kaart{Bekijk statistiek kaart F:   Schat het percentage mensen dat als lievelingseten spaghetti opgaven, je mag er slechts $ 2% $ langs zitten. } { $ 11% $}} What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit? Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets Let $X$ de a vector space and $A\subset X$. If we define $A+B :=\{a+b|a\in A, b\in B\}$ I am trying to show that    $$ \begin{equation} 2A \subsetneq A+A, \end{equation} $$  i.e., it might happen that $2A \neq A+A$. I was able to show that $2A \subset A+A$, but I am not able to come up with a counterexample to show that the converse is not necessarily true. If I assume $A+A\subset 2A$ and let $x\in(A+A)$, then by its definition we have $x=a_1 + a_2$ for some $a_1,a_2\in A$ I guess I could naively say that $a_1+a_2 = 2(a'_1+a'_2)$ where $a_i=a_i/2$ for $i=1,2$ and I guess $(a'_1+a'_2)$ might not be an element of $A$ in some concrete case but I am not able to come up with anything and I've spent more time than I would like to admit. Any suggestions?  Thank you. Notation: Why write the differential first? What size difference is there between the PSP 1000, 2000 and 3000 for applying Skin Stickers? Using conditional statements in ArcGIS Field Calculator? I have two fields, "P_Area" and "PC_Area", whose sizes I'd like to compare in a third field, "Areas_Equal". The "Areas_Equal" field should contain a "Yes" if the other two are equal and a "No" if they aren't.  How can I do this with Field Calculator and its Python Parser? Is Borden's true identity real, or another ruse? Towards the end of , it's revealed that Borden accomplishes his Transported Man trick by using his twin brother, Fallon, as a double. It then becomes clear that he has been doing this in his personal life as well as on stage - each brother leads 'half a life', sometimes appearing as Borden and sometimes as Fallon. This is how he completes the illusion: one Borden goes into the first door, the other Borden emerges from the second door a moment later. Angier doesn't know how Borden does the trick, and doesn't believe Borden uses a double despite being told as much by Cutter. He follows what he believes to be a clue in Borden's notebook and travels to Colorado to meet Nikola Tesla, who Angier believes can build a machine that can help him perform the trick. Angier believes that Tesla built a similar machine for Borden. However, the final pages of the notebook reveal that Tesla was merely a red herring, designed to get Angier out of Borden's way for a long time. Tesla, it turns out, had never built such a machine before. At this point, Tesla agrees to build Angier's machine anyway. Instead of building a machine that transports matter, he builds one that duplicates it. Angier uses this machine in his act, but in order to avoid having to deal with multiple clones (the &quot;prestige materials&quot;), one of them must die as part of the act. This all makes sense, so far, but I find it hard to believe that Borden's use of the word 'Tesla' as the key to his cipher is random. It's too coincidental that he sends Angier on a wild goose chase, but Angier returns with a working machine. A film that is otherwise so tightly plotted shouldn't rely on coincidence to move the narrative forward, so there must be something else going on. Is it possible that Borden cloned himself using Tesla's machine? What is the www-data user? How do I start DMing a new game after the Red Box? If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$ How do I force TeX to completely use the 1st column before writing to the second column?  Right now I dont have enough content to fill one whole page. So the left and right columns are equally filled, leaving 25% symmetrical empty page at bottom. How do I fill the left column first, and then the right?  \documentclass{article}  \usepackage{multicol} \usepackage[scale=0.9]{geometry} \usepackage{amssymb} \renewcommand{\labelitemi}{\tiny$\blacksquare$} \begin{document} \begin{multicols}{2}      %lots of text goes here  \end{multicols} \end{document} What is the rigor behind U subsitution? $ \int f(g(x)) dx = \int \frac {f(u)}{u'} du$  requires that  $ \int f(x) dx = \int f(x) \cdot dx$  but dx just represents the variable that F(x) +c is a function of. So why is it legal for dx to be treated algebriacally?  I tried investigating this property by using riemann summation:  $\lim\limits_{n \to \infty}(\sum_{k=1}^n f(\frac{kx}{n} )\frac{x}{n}) = \int_0^x f(t)dt= (F(x)+c)-(F(0)+c)$  and so you can define   $ \lim\limits_{n \to \infty} (\sum_{k=1}^n f(\frac{kx}{n} )\frac{x}{n})+F(0)+c)  = \int f(x) dx$  you can write $\frac{x}{n} = dx$ and $k\frac{x}{n}=kdx= x_k$  then you have  $ \lim\limits_{n \to \infty} (\sum_{k=1}^n f(x_k)dx)+F(0)+c) = \int f(x) dx$  since  dx is being written to be multiplied by the series, then you can define dx in different terms to aquire an integral in terms of other variables.   but that exists only in abstraction. I can't quite sufficiently complete the task of doing so. Max or Default? What is the best way to get the Max value from a LINQ query that may return no rows? If I just do  Dim x = (From y In context.MyTable _          Where y.MyField = value _          Select y.MyCounter).Max   I get an error when the query returns no rows. I could do  Dim x = (From y In context.MyTable _          Where y.MyField = value _          Select y.MyCounter _          Order By MyCounter Descending).FirstOrDefault   but that feels a little obtuse for such a simple request. Am I missing a better way to do it?  UPDATE: Here's the back story: I'm trying to retrieve the next eligibility counter from a child table (legacy system, don't get me started...). The first eligibility row for each patient is always 1, the second is 2, etc. (obviously this is not the primary key of the child table). So, I'm selecting the max existing counter value for a patient, and then adding 1 to it to create a new row. When there are no existing child values, I need the query to return 0 (so adding 1 will give me a counter value of 1). Note that I don't want to rely on the raw count of child rows, in case the legacy app introduces gaps in the counter values (possible). My bad for trying to make the question too generic. Determining Min - Max within zip code (statistics by area)? I'm new to ArcGIS Desktop. I have created a layer representing zip codes and overlayed it with a layer containing some data points. I want to find the min and max value of the data points in each zip code. Currently, I am manually checking the values if all the data points in each zip code but this is becoming very time-consuming and cumbersome.   Is there a faster way to do this? A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it.   Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too.  My question is: What is the work done by the the battery?  According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity? When the automorphism group is trivial...... If $G$ is a trivial group , obviously $Aut(G)$  is  trivial . Does the converse  hold $?$ .  When  we  are  given  that a  group $G$  has  trivial  automorphism  group , can we  conclude  that the group  will  be  trivial $?$ .  I  guess  not . For  one  thing , we know  that  $$G/Z(G)\cong Inn(G)$$. So , $Aut(G)$ being  trivial  would  imply  that $$G\cong Z(G)$$  i.e.  $G$  is  commutative . But I  see  nothing about $G'$s being trivial .   The problem  is  that  while I cannot  prove  it , I  could  not  find  a  counter example  either , from  among  the  groups  I  am  familiar  with .   What  is  the non-trivial  commutative  group  that  has  trivial  automorphism  group  $?$ Adding admin-ajax.php to the frontend. Good or bad idea? I love admin-ajax.php. But I hate having to localize in order to point frontend scripts to it, and I wish there was an equivalent, easy-to-find file for themes. (It also just bothers me to see frontend requests go through "/wp-admin/". No practical reason, just looks ugly IMO.)  So I've simply copied admin-ajax.php to the root dir at "/ajax.php", adjusted the include paths and removed the WP_ADMIN constant definition. Seems to work like gangbusters (I can now just direct all my frontend AJAX requests to /ajax.php! And I can still use the normal wp_ajax hooks in my plugins!).  But is this safe? What might go wrong? Since this isn't built into core, I assume there's a good reason as to why not. But looking through the code, I can't see any immediate problems.   You're smart--tell me if this approach is crazy. Or if there's a simpler method that I'm overlooking.