A  proposes Practiced Spellcaster to keep increasing the more valuable (Wizard) class.   The Practiced Spellcaster feat (Complete Arcane, p. 82) increases CL by 4, up to the character level. The  prestige class increases CL at levels 1, 4, 7 and 10, without any such limitation.   Can I count Practiced Spellcaster first, to reach my class level, then increase it by four, or is the feat completely wasted, is the difference between my CL and character level less than 4?
I have seen quoted several places on the internet a rule that one can apply bonuses and penalties in the most beneficial order.  An example I come across frequently (as a druid) is the combination of Natural Bond and . Natural Bond increases your effective druid level for determining the stats of animal companions but cannot increase it beyond your character level. Choosing an alternative animal companion lowers your effective druid level for determining the same stats. The "most beneficial order" rule is used to justify applying the level penalty before the natural bond bonus in order to get around the character level cap on natural bond.  Does this rule actually exist? If so, where does this rule originate? I would like to be able to cite a reliable source for my GM.
The difference between try/catch/throw and try/catch(e)/throw e Is there a bulletproof way to know a file has been successfully decrypted? I am wondering whether there is a bulletproof way to know if one is successful in decrypting a file.   As an example, say I encrypt a text file and protect it with a 3 letter password. I use brute force to decrypt it, but two different passwords lead to a file that contains English intelligible text. Is there a way for me to know which one is the original one? In other words, is there an infallible way to know I've entered the password correctly? How does asymmetric encryption work? I've always been interested in encryption but I have never found a good explanation (beginners explanation) of how encryption with public key and decryption with private key works.  How does it encrypt something with one key and decipher it with another key? Change line spacing inside a node in TikZ About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$ Let $q: \mathbb{N} \to \mathbb{Q}$ be a bijection and denote the image of $k \in \mathbb{N}$ by $q_k$.  Let $f: \mathbb{R} \to (0,1)$, $$ f(x) = \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} $$  Show that:  1) $f$ is strictly increasing  2) $f$ is continuous at $x$ iff $x \in \mathbb{R} \setminus \mathbb{Q}$.  My work:  Let $x, y \in \mathbb{R}$, $x &lt; y$. Then there exists $q_n \in \mathbb{Q}$ s.t. $x &lt; q_n &lt; y$. Now $$ f(x) = \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} &lt; \underset{q_k \leq x}{\sum_{k \in \mathbb{N}}} 2^{-k} + 2^{-n} \leq \underset{q_k \leq y}{\sum_{k \in \mathbb{N}}} 2^{-n} = f(y) $$ so $f$ is strictly increasing.  I think my proof of 1) is ok, but how can I prove 2)? "It is not possible to check out a single file. The finest level of checkouts you can do is at the directory level."  How do I get around this issue when using Subversion?  We have this folder in Subversion where we keep all our images. I just want to check out one file (image) from that. This folder is really big and has ton of other stuff which I don't need now. No space following macro without argument With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space? I am wondering whether there exists a function such that:  $$\lim_{x \rightarrow a}f(x)=\infty$$  at some point $a$ on the real axis but yet,  $$\int_{-\infty}^{+\infty}\left|f(x)\right|\ dx&lt;\infty$$  Does the fact that a function is unbounded imply that it has no finite integral? Permission Subscribe to Dashboards: Add Recipients depends on permission(s): Subscribe to Dashboards UMVUE of $e^{-\lambda}$ from poisson distribution Let $X_1,\ldots,X_n \sim$ Poisson$(\lambda)$. I wish to find UMVUE of $e^{-\lambda}$. Here $\overline{X}_n$ is complete and sufficient for $\lambda$ (hence for $e^{-\lambda}$??). Define $Y_i=1$ if $X_i=0,$ $Y_i=0$ otherwise. Clearly (I checked!) each $Y_i$ and hence $\overline{Y}_n$ is unbiased for $e^{-\lambda}$. Then I should be able to use the Lehmann Scheffe theorem to deduce the UMVUE. The estimator I get looks like $$\frac{1}{n} E\left\{\#X_i:X_i=0 \mid \sum_{i=1}^n X_i\right\}$$ whereas the correct answer is $$\left(\frac{n-1}{n}\right)^{\sum_{i=1}^n X_i}$$ I'd appreciate if anyone lets me know where I'm going wrong and guides me into the right path. Thank you. How was Hedwig able to find Sirius? In the beginning of Goblet of Fire, Harry sends Snuffles a letter.  Hedwig somehow finds him after the extremely specific command from Harry, "Just find him, okay?"   Theories:   Hedwig has a scanning system, like Baymax in Big Hero 6. Hedwig got super lucky. Hedwig flies really, really fast.   Now I know that owls are intelligent beings in the Harry Potter canon. But.... those ideas are just as crazy as the next.  So how did Hedwig do it? command to display time (duration) in human readable form I spent 3 hours trying to write a command to format a time (duration) expressed as a floating number (in seconds) in a nice form as follows:  if the time is &lt; 60 write as a float with 3 decimals (i.e. milliseconds)  else let h,m,s be the hours, minutes and seconds corresponding to the time      if h=0 then write as m:ss (ss always with 2 digits, m can have only 1)      else write h:mm:ss (mm and ss with 2 digits, h can have only 1)   So 1.25678 gives 1.256, 125.35 gives 2:05, 18249 (which equals to 5*3600+4*60+9) gives 5:04:09.  I tried several packages for the comparison/formatting. No success. Can someone help me ? Thanks ! How to compress entire drive C in Windows including locked files? Positive correlation and negative regressor coefficient sign Is it possible to obtain a positive correlation between a regressor and a response (+0,43) and, after that, obtain a negative coefficient in the fitted regression model for this regressor?  I'm not talking about changes in the sign of the regressor among some models. The coefficient sign always remains.  Could  the remaining variables of the fitted model influence the changing of the sign? Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded? Brightness changes while "Adaptive Brightness" is disabled in Windows 8.1/10 with Intel HD Graphics The brightness changes with the colors displayed on the screen on my Lenovo Thinkpads with Intel HD Graphics. Light colors make the screen brighter, dark make it darker. Same behavior in Windows 8.1 and 10.  The "adaptive brightness" feature in Windows is disabled. Call to a member function on a non-object So I'm refactoring my code to implement more OOP.  I set up a class to hold page attributes.  class PageAtrributes  {   private $db_connection;   private $page_title;      public function __construct($db_connection)      {         $this-&gt;db_connection = $db_connection;         $this-&gt;page_title = '';     }      public function get_page_title()     {         return $this-&gt;page_title;     }      public function set_page_title($page_title)     {         $this-&gt;page_title = $page_title;     } }   Later on I call the set_page_title() function like so  function page_properties($objPortal) {         $objPage-&gt;set_page_title($myrow['title']); }   When I do I receive the error message:     Call to a member function set_page_title() on a non-object   So what am I missing? I heard that there was a twitter bot which automatically posted questions and asked for answers for specific questions on every site. How do they work? Is there an algorithm for doing this or is it purely random? I know that it doesn't tweet closed questions, but that's it. I am looking for idioms or informal/slang/colloquial expression for some people that make you think that they are able of building a skyscraper, constructing a spaceship, playing the piano better than Mozart or something very fancy that requires remarkable skills, but when it comes to practice they prove to be completely inadequate. 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.