Prog 1:   #include&lt;stdio.h&gt;  int main()  {      int i=0;      while(i&lt;=8,i++);      printf("%d",i);      return 0;   }   Prog 2:  #include&lt;stdio.h&gt;  int main() {   int i=0;   while(i++,i&lt;=8);   printf("%d",i);   return 0; }   The output of Prog 1 is 1 and that of Prog 2 is 9.  Can someone explain whats going here. How the two codes are different?
What does the , operator do in C?
For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$. Can someone please verify my proof or offer suggestions for improvement? I am aware that there is a similar question elsewhere, but I want help with my proof in particular.     Let $T_1, \ldots, T_k$ be subtrees of a tree $T$ such that for all $1 \leq i &lt; j \leq k$, the trees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.   Suppose, for the sake of contradiction, that for every vertex $v \in V(T)$, there is a subtree $T'$ in the list $T_1, T_2, \ldots, T_k$ such that $v \notin V(T')$.  Pick $v_1 \in T_1$. There is a subtree $T^{(1)}$ such that $v_1 \notin T^{(1)}$. $T_1$ and $T^{(1)}$ have a vertex $y_1$ in common. Now, there exists a tree $T^{(2)}$ such that $y_1 \notin T^{(2)}$. But now, $T^{(2)}$ and $T^{(1)}$ have a vertex $y_2$ in common. Also, $T_1$ and $T^{(2)}$ have a vertex $y_3$ in common.  There exists a path $p_1$ in $T_1$ from $y_3$ to $y_1$. Also, there is a path $p_2$ in $T^{(1)}$ from $y_1$ to $y_2$ and a path $p_3$ in $T^{(2)}$ from $y_2$ to $y_3$. Note that the path formed by the union of $p_1$ and $p_2$ passes through $y_1$, while $p_3$ does not, since $y_1 \notin T^{(2)}$. Therefore, the union of $p_1, p_2$, and $p_3$ forms a cycle, contradicting the fact that $T$ is a tree. Therefore, it must be the case that there is a vertex $x$ in all of the $T_i$. SQL Query; Admin Log System; Foreign Keys; Retriving multiple rows form different tables at once Table A (users)  id     | name   | ip 52433    Yashas   1.1.1.1 512      Admin    5.6.7.8   Table B (admin_record)  id    | admin | time    | date    | reason | action  52433   512     2312352   1213213   Test     WARN   id is FOREIGN key  Table B keeps a log of all actions an administrator takes on his users. And the table A stores the account information of the users &amp; administrators.  I am trying to display a list of actions taken by a administrators on a user.   I want to write a query which gets me all the rows of table B where id = fixed number.  Here is what I want to display:  "Administrator1 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX. "Administrator2 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX. "Administrator3 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX.   All I have is the user's id using which I need to obtain all the entries in the log along with the administrator names. I need to obtain the admin's name, users name and all the contents of table B related to a particular user in one single query. If possible, I want the to change the field name(not literally change, but want the SQL server to send the data with new field names to separate admin name &amp; user name) of the admin's name to admin_name and user's name as . I mean something like this  SELECT users.name AS admin_name WHERE users.id = %i  AND SELECT users.name AS user_name WHERE users.id = %i   (the query isn't correct,it us just an example to show what I am trying)  Progress so far:   SELECT player.name, player.ip, admin.name, record.date, record.time, record.action, record.reason FROM admin_record AS record JOIN users AS player ON player.id = record.id JOIN users AS admin ON admin.id = record.admin WHERE player.id=%i   where admin_record is table B &amp; users is table A. G-test vs Pearson's chi-squared test Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$ Let $(I_n)_{n \geq 1}$ be a sequence such that: $$I_n = \int_0^1 (1-x^2)^n dx$$  Find the value of $I_n$ (The solution is $\frac{2}{3} \cdot \frac{4}{5} \cdot ... \cdot \frac{2n}{2n+1}$).  I've tried using the binomial expansion of $(1-x^2)^n$ but I couldn't get the proper answer.  Thank you! Can you combine multiple lists with LINQ? Say I have two lists:  var list1 = new int[] {1, 2, 3}; var list2 = new string[] {"a", "b", "c"};   Is it possible to write a LINQ statement that will generate the following list:  var result = new []{      new {i = 1, s = "a"},     new {i = 1, s = "b"},     new {i = 1, s = "c"},     new {i = 2, s = "a"},     new {i = 2, s = "b"},     new {i = 2, s = "c"},     new {i = 3, s = "a"},     new {i = 3, s = "b"},     new {i = 3, s = "c"} };   ?  Edit: I forgot to mention I didn't want it in query syntax. Anyway, based on preetsangha's answer I've got the following:  var result = list1.SelectMany(i =&gt;  list2.Select(s =&gt; new {i = i, s = s})); If an effect would prevent a spell from doing damage, does it continue to prevent that damage after the spell changes zones? Anthony casts , targeting Nathan's .  Nathan casts and resolves , choosing to 1) prevent all damage that would be dealt by Searing Blood this turn and 2) put a +1/+1 counter on Elvish Mystic.  Searing Blood resolves, deals no damage, and goes to the graveyard.  Anthony casts and resolves  to kill Elvish Mystic.  Searing Blood triggers from the graveyard, because Elvish Mystic died. Does the prevention effect created by Dromoka's command still apply to it after it changes zones? In other words, will Searing Blood deal 3 damage to Nathan? Covariance of binary and continuous variable Suppose $y$ is a continuous random variable and $d$ is a binary random variable that takes the value $1$ with probability $p$ and $0$ with probability $1-p$.   How do I show that $\text{Cov}(y,d)=(E[y|d=1]-E[y|d=0])p(1-p)$? Maven artifact and groupId naming Sum of nth roots of unity Question: If $c\neq 1$ is an $n^{th}$ root of unity then, $1+c+...+c^{n-1} = 0$  Attempt: So I have established that I need to show that $$\sum^{n-1}_{k=0} e^{\frac{i2k\pi}{n}}=\frac{1-e^{\frac{ik2\pi}{n}}}{1-e^{\frac{i2\pi}{n}}} =0$$ by use of the sum of geometric series'. My issue is proceeding further to show that this is indeed true. Whilst I understand how the RSA algorithm works, I don't understand how the CPU operates when it needs to use the mod function with a huge number $n$, for example.  $n = 8192$ bits; $c = m^e \mod n$;  In essence my question is how does the CPU deal with this huge modulus? How can I change (or remove / reset ) my name on a site in Stack Exchange network? Printing a file to a printer in Ruby Let $G$ be a finite group and $F$ a field with $\mathrm{char}(F)=0$ or coprime to $|G|$. Let $V$ be a $FG$-module in a way that every $ FG$-homomorphism $ f : V \to V $ is given by $f(x)= \lambda x $. Then $V$ is irreducible.   I already managed to proof this by contradiction, using Maschke's Theorem. We can  write $V$ as $U\oplus W$ and get a $FG$-homomorphism $\pi:U\oplus W \to U\oplus W$, $\pi (u+w)=u$, then $\pi(u+w)=\lambda (u+w)=u $ then either $U$ or $W$ are trivial and thus $V$ is irreducible.  My question is if this statements still holds if the characterictic of $F$ divides the order of $G$, since I only used this fact in my proof to use Maschke's theorem. Let $p$ be a prime number, and let $\mathbb{F}_p$ be the field with $p$ elements. How many elements of $\mathbb{F}_p$ have cube roots in $\mathbb{F}_p$?   I had this question on an exam and after reviewing I am still not sure. Any help would be appreciated. What is the best practice to make division return double in C# In c# when you want to divide the result of a method such as below, what is the best way to force it to return a double value rather than the default integer.   (int)Math.Ceiling((double)(System.DateTime.DaysInMonth(2009, 1) / 7));   As you can see I need the division to return a double so I can use the ceiling function. If $f'$ is differentiable at $a$ then $f'$ is continuous at $(a-\delta,a+\delta)$ I have a python list, say l  l = [1,5,8]   I want to write a sql query to get the data for all the elements of the list, say  select name from students where id = |IN THE LIST l|   How do I accomplish this? How to add a class to a given element? I have an element that already has a class: &lt;div class=&quot;someclass&quot;&gt;     &lt;img ... id=&quot;image1&quot; name=&quot;image1&quot; /&gt; &lt;/div&gt;  Now, I want to create a JavaScript function that will add a class to the div (not replace, but add). How can I do that? Given an instance of System.Reflection.Assembly. Are repository lists secure? Is there an HTTPS version? Are repository updates secure?  As a bear of little brain from the developer side, I cannot understand why the repository list is http://security.ubuntu.com and the other http(unsecured) sites listed in /etc/apt/sources.list.  Without a certificate chain match this appears as "ask any responder for a list of packages to update" instead of "ask the ubuntu.com site..."  Can any network choose to spoof the update sites, and is this a common practice to provide a locally cached and vetted copy?