What's the rule for a natural 20 on a Perception check?
How does DC work with natural 20?
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed? Prove $$\det(e^A) = e^{\operatorname{tr}(A)}$$ for all matrices $A \in \mathbb{C}_{n×n}$. Is being good at mathematic contests necessary to pursue a career in mathematics or physics? I am extremely poor in solving a problem quickly, which leaves me doing badly in olympiads and other contests. But, if I just don’t give up on a problem, no matter how much time it takes, I usually end up solving it. To have a future in mathematics or physics, is it necessary for me to excel at contests, because these days children excelling at contests have an advantage over those who don’t (not complete advantage, but advantage nonetheless)? How can I test whether a command's output is an empty string while not   interfering with buffering?  Example:  command | ??? if [ $? = 0 ] &amp;&amp; [ -n "$output_from_command"]; then    ...   I want the output from the code above to be the same as when running command. Conveying "under the radar" in a less colloquial way I am searching for a word to contrast with iconic  I want to characterize views of the city as both iconic and under the radar, maybe "non-iconic."  I was thinking about saying that a view of the city was undiscovered, but I think that maybe that overstates what I'm think-- I more mean under-appreciated. Are there any other words that come to mind? Why is the gap between the translation and the last line of the gloss so wide in my interlinear gloss? I have come across this .  Has anyone tried anything similar or does it work for you? Can you tell if an email customer / user enters is correct &amp; exists? Is "funnest" a word? How does wizard & cleric spell preparation and casting work? In 3.X wizards had spellbooks, while clerics had their entire spell list, but they both memorized/prepared spells every day from those lists, and had a certain number of slots for preparing spells in.  Now in 5e preparing spells and spell slots aren't the same thing. What's going on here? How does their spellcasting work now? return eats exception I found the following behavior at least weird:  def errors():     try:         ErrorErrorError     finally:         return 10  print errors() # prints: 10 # It should raise: NameError: name 'ErrorErrorError' is not defined   The exception disappears when you use return inside a finally clause. Is that a bug? Is that documented anywhere?  But the real question (and the answer I will mark as correct) is: What is the python developers' reason to allow that odd behavior? Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device. How to prove that a simple graph having 11 or more vertices or its complement is not planar? It is an exercise on a book again. If a simple graph $G$ has 11 or more vertices,then either G or its complement  $\overline { G } $ is not planar.  How to begin with this? Induction?  Thanks for your help! How do I join two lists in Java? Identification of mid-80s time travel tv show Is it better in C++ to pass by value or pass by constant reference? Is it better in C++ to pass by value or pass by constant reference?  I am wondering which is better practice.  I realize that pass by constant reference should provide for better performance in the program because you are not making a copy of the variable. Wouldn't multiple filters in a convolutional layer learn the same parameter during training? Based from what I have learned, we use multiple filters in a Conv Layer of a CNN to learn different feature detectors. But since these filters are applied similarly (i.e. slided and multiplied to regions of the input), wouldn't they just learn the same parameters during training? Hence the use of multiple filters would be redundant? What happened to Startups SE? I really enjoyed that site. I've only posted on it once, but I enjoyed seeing other people's posts and appreciated reading about entrepreneurial dilemmas. what is wrong with this??? please,can anyone help?  \begin{equation} \label{probabilityy} P^{t}({E_{0})=P_{0}+(1-P_{0})P_{1}+ (1-P_{0})(1-P_{1})P_{2}+.......+P_{n}\Pi_{k_{0}}^{n-1}(1-P_{k}) \end{equation} How to avoid ArrayIndexOutOfBoundsException or IndexOutOfBoundsException? What is the terminology for data aggregated via summed totals versus data aggregated via means? The two types of data differ in that if you decide to decrease the temporal (time) resolution of the first type of data you take the mean of lower the resolutions. With the second you take the sum over the lower resolutions. Here is a concrete example  Gas Used (kWh), Outside Air Temperature (C), Time Resolution (Minutes) 100, 20, 20 140, 22, 20 120, 21, 20   Here the hourly (60 Minute) resolution data is clearly  360, 21, 60   and is found by averaging the temperature and summing up the gas used.  What I really wish to know is what the names for each of these types of data are called. I understand that this question is not the best but it is hard to ask a question about something whose names you do not know. If you have a better way of articulating the question then please go ahead and edit it.