equivalent versions of axiom of choice
Power set equivalency of Axiom of Choice
In D&amp;D 5e &quot;&quot; is a condition that can affect a creature during the first round of combat, only until the end of their turn:  [... T]he GM compares the Dexterity (Stealth) checks of anyone Hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn’t notice a threat is surprised at the start of the encounter. If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends. A member of a group can be surprised even if the other members aren’t. - PHB 189  Does the action that causes the surprise count as part of the round, though? Say Renee, a rogue, achieves a stealth check of 22, easily beating an orc sentry's passive perception. She sneaks directly behind him and stabs him in the back. Surely the orc isn't surprised at all until the dagger hits him (or if Renee misses, she fumbles around behind him or something). What I think it really boils down to in the end is: when is initiative rolled? If (in our example) initiative is rolled before Renee's attack hits (or misses) how can we justify the orc recovering from his surprise before the action that triggered said surprise even occurs, should he roll better than Renee on his initiative? I'd like to go with initiative is rolled immediately following whatever event began the encounter (which could be an attack, but is likely to often be something else wherever surprise isn't intended), but I can't find any documentation to support this stance.  Why Does Anyone Care? There are many reasons you might want someone to be surprised while you're attacking - in this example if Renee is over L3 (and took the Assassin archetype) she'll get 'Assassinate' if the orc is surprised, and 'Death Strike' if she's over L17. That's a lot of potential extra damage!  that if the orc is surprised, Renee will be able to retreat and hide, without having to take the disengage action as her bonus action to avoid an attack of opportunity. Of course, there's no way for her to know whether the orc is surprised or not at that stage, so trying this would be a bit of a gamble... Geometric random variables $X_1:G(p_1)$ $X_2:G(p_2)$ $X_3:G(p_3)$ are independent, prove the following : I checked the other question similar to this issue yet I could not find a proper solution for the issue I am facing for including an .svg file which is converted using inkscape with pdf+latex option set to ON, and I have also included both the .pdf and .pdf_tex file in the path. Yet I get the above mentioned error.   My code:  \begin{figure}[h!]  \centering \def\svgwidth{\columnwidth} \input{Implementation/Figs/most_changed_from_default_pos_0.pdf_tex} \end{figure}   Full error description:  !pdfTeX error: pdflatex (file /compile/Implementation/Figs/most_changed_from_default_pos_0.pdf): PDF inclusion: required page does not exist &lt;5&gt;   Any help to solve this issue would be really appreciated. I also downloaded the pdf file to check whether it has 5 pages. I could verify it, there were 5 pages in the pdf file.   The file which I want to convert is   I have added the google drive link to the file which I have used for analysis herewith Field extensions and algebraic/transcendental elements Let $E$ be an extension of field $F$, and let $\alpha, \beta \in E$. Suppose $\alpha$ is transcendental over $F$ but algebraic over $F(\beta)$.   Show that $\beta$ is algebraic over $F(\alpha)$.  Okay, first questions: What does the notation $F(\alpha)$ and $F(\beta)$ mean? And being transcendental means it solves no equations with rational coefficients, but what does it mean for a field? Can Yoda pilot a starfighter? In a trailer for Kinect Star Wars, I saw Yoda driving a Jungle Speeder and that got me wondering. Can and has Yoda ever piloted a starfighter?  During the Clone Wars, it seems plausible that they could commission a small-sized green Jedi starfighter. Is their any indication that he has piloting experience? So  i have a scene with a few objects, and a water simulation in the scene. However I want to animate the camera turning around in the scene, while the water simulation is frozen in time. So something like a time freeze effect. But when ever I try to render an animation it renders the water simulation too. I just need one frame of the water simulation. Is there a way to do this? Monitor cell value and copy it to another cell White background with filmic blender When I tried to connect my Ubuntu 13.10 to my VM Centos 6.5 using ssh appear the message "Connection refused" or "No route to host" even than I change the port, noting change.    I need to use SSH, VPN and Samba, but this IP in my VM Centos do not work.  How Can I resolve this problem? Normal subgroup of a normal subgroup Let $F,G,H$ be groups such that $F\trianglelefteq G \trianglelefteq H$.  I am asked whether we necessarily have $F\trianglelefteq H$. I think the answer is no but I cannot find any counterexample with usual groups. Is there a simple case where this property is not true? Evaluating string "3*(4+2)" yield int 18 Configuring dpkg stops processing when calling an HTTP request to Adobe Flash Player I recently moved to Linux, and I am in love with the experience. Opinions apart, I am having problems when running sudo dpkg --configure -a  My computer stops processing the command here:  You may know Adobe Flash Player is no longer supported, and I believe that could be why the command is unable to load pepperflashplugin-nonfree. I have tried fixing the problem by checking older posts here, but none of them was able to fix this problem. I run processing.run(&quot;native:buffer&quot;) and from newly created vector I get all features and export them to string using QgsJsonExporter(). My problem is that newly created vector gives new IDs to all features and they aren't equal to attribute ID's values. And after exporting them to GeoJSON using QgsJsonExporter() I get GeoJSON features with identifiers. However I can solve this by declaring processing.run(&quot;native:buffer&quot;) algorithm OUTPUT to .geosjon file and opening it afterwards. Is there a way that I can get GeoJSON string without IDs without having to save OUTPUT to .geojson and reading it to string afterwards. vl = QgsVectorLayer(sys.argv[1],&quot;mygeojson&quot;,&quot;ogr&quot;)  def runProcessingNativeBuffer(inputGeoJson, distance):     processing.algorithmHelp(&quot;native:buffer&quot;)     return processing.run(&quot;native:buffer&quot;,                          {'INPUT': inputGeoJson,                           'DISTANCE': distance, 'SEGMENTS': 5,                           'END_CAP_STYLE': 0, 'JOIN_STYLE': 0,                           'MITER_LIMIT': 2, 'DISSOLVE': False,                           'OUTPUT': &quot;TEMPORARY_OUTPUT&quot;})  ats = runProcessingNativeBuffer(vl, sys.argv[2])  vl1=ats['OUTPUT']  features = vl1.getFeatures() exporter = QgsJsonExporter() print(&quot;GEOJSON&quot;,exporter.exportFeatures(features))  IDs in properties are fine I don't need additional IDs in &quot;features&quot; Java - Screen turns black, when setting a JFrame to Fullscreen Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:  In analytic (Lagrangian) mechanics, the derivation of the Euler-Lagrange equations from the principle of least action assumes that the start and end coordinates at the initial and final times are known. As a consequence, any variation on the physical path must vanish at its boundaries. This conveniently cancels out the contributions of the boundary terms after integration by parts, and setting the requirement for minimal action, we obtain the E.L. equations.  This is all nice and dandy, but our intention is finding the location of a particle at a time in the future, which we do not know a priori; after we derive any equations of motion for a system, we solve them by applying initial values instead of boundary conditions.   How are these two approaches consistent? The context for my question might be a bit strange.   I have stuttering and therefore I have some difficulties pronouncing some words starting with particular phonetics. And I've found that if a sentence starts with a /th/ sound, it makes me feel uncomfortable.  Especially in the word is "thanks" or "thank you".  So I want to know if there's a popular alternative for "thank you" that may not seem strange and that unnatural. I've searched the website and I know there are alternatives like "I appreciate your help." but that sounds a bit overly formal for me. (Or is it? correct me if I'm mistaken.) solving diophantine equations using congruences So, a question in Elementary Number Theory by David M. Burton:     Problems 4.4      2(a) Using congruences, solve the diophantine equation 4x + 51y = 9       Hint: $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$, whereas $ \ 51y \equiv 9 (mod \ 4)$ gives $y = 3+4s $. Find the relation between $s$ and $t$ From this hint, I substitute $ x = 15 +51t$ and $y = 3+4s$ in the given equation $4x + 51y = 9$ to get the relation $s = -t-1$ and using which I can get the solutions $ x = 15 + 51t, \ y =-1-4t$ But we know that the solutions of $ax \equiv b (mod \ n)$ is equivatent to the solutions of the diophantine equation $ax -ny = b$, so, solutions of $4x \equiv 9(mod \ 51) $ is equivalent to solutions of the equation $4x-51y=9$ whereas, solutions of $51y \equiv 9(mod \ 4) $ is equivalent to solutions of the equation $-4x+51y=9$ Now, my question is: as, the above equations $4x-51y=9$ and $-4x+51y=9$ are different, then what is the point of substituting $ x = 15 +51t$ (solution of $4x-51y=9$) and $y = 3+4s $ (solution of $-4x+51y=9$) in the given equation $4x+51y=9$ to find a relation between $t$ and $s$ ? Isn't it absurd as $ x = 15 +51t$ and $y = 3+4s $ are solutions of two different equations? Can anyone please explain this? PS: I did it like this $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$ and by substituting it in $4x+51y=9$ we get $y=-1-4t$ Get the generated SQL statement from a SqlCommand object? I have the following code:  Using cmd As SqlCommand = Connection.CreateCommand     cmd.CommandText = "UPDATE someTable SET Value = @Value"     cmd.CommandText &amp;= " WHERE Id = @Id"     cmd.Parameters.AddWithValue("@Id", 1234)     cmd.Parameters.AddWithValue("@Value", "myValue")     cmd.ExecuteNonQuery End Using   I wonder if there is any way to get the final SQL statment as a String, which should look like this:  UPDATE someTable SET Value = "myValue" WHERE Id = 1234   If anyone wonders why I would do this:   for logging (failed) statements for having the possibility to copy &amp; paste it to the Enterprise Manager for testing purposes Showing that a sequence is monotone and thus convergent Here's the original question:     Let $(a_n)$ be bounded. Assume that $a_{n+1} \ge a_{n} - 2^{-n}$. Show   that $(a_n)$ is convergent.   Okay, I know that if I can show that if the sequence is monotone, I can conclude that it is convergent. But I am not sure how to show that it is monotone.  I know that  $$a_n \le a_{n+1} + \frac{1}{2^n} &lt; a_{n+1} + \frac{1}{n}$$  It looks to me as if it is monotonically increasing but I'm quite not sure how to prove my claim. Any hints would be appreciated. Where to download Flash Player for offline installation? I can't find Flash Player download link which will give me the full EXE/MSI file, not the tiny downloader which downloads data from the internet.  What's the proper download site for this?