Unable to type ⱱ with tipa
The IPA symbol for the labiodental flap (ⱱ)
I was pondering a bit more about  question regarding being able to &quot;omit&quot; the base case in a proof by strong induction due to vacuous truth. The post states:  Strong induction proves a sequence of statements $P(0), P(1), …$ by proving the implication &quot;If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true.&quot; for every nonnegative integer $n$. There is no need for a separate base case, because the $n=0$ instance of the implication is the base case, vacuously.  However, if we consider $n=0$, we would have that the statement is vacuously true, which I would take to mean that the implication is true regardless of the validity of $P(0)$. However, clearly it's necessary for $P(0)$ to hold for an induction proof to be valid. So I'm confused on how, by omitting the base case, $n=0$ isn't just a tautology, making the implication true regardless of whether $P(0)$ actually holds. What does this depiction of a black hole in the movie Interstellar mean? I was expecting a whirlpool in 3D and the matter glowing from friction as it nears the center, as I expected a event horizon to be negligible visually.  How does this depiction work? How big is the central sphere? I am puzzled by the perpendicular circles. Are they the event horizons if they are both visible? What would be a path of a particle as it gets swallowed into the singularity? How to open a new Terminal with shell prompt and running multiple commands in Command Line? I want to Open a new Terminal in from within terminal.  It should have Shell prompt as well as already run few commands.  How to do it ? What is the meaning of this two letter code in the YouTube logo? I see a new logo with CA at youtube.com. Does anyone know what it means? Cannot sort on numeric field with SOQL in Custom Metadata Cannot sort on a soql-request in a custom meta data type. When i perform SELECT .. FROM x__mdt WHERE ... ORDER BY x. Then field x cannot be numeric to get a correct order. Change it to a string-field ordering works ok. Playing with ASC/DESC makes no difference! Lead in ice block This is a strange question I would like to have some explanation accompanied with:  We have an ice block, with in it a lead block. This entire block is put into a glass of water, resulting in a rise of water level until the edge of the glass. The block stays floating on the surface. What will happen with the water level when the ice melts?  The answer is that it will drop, but how is this even true?? My thoughts are: - block floats on water, so rho(block) &lt; rho(water) - Archimedes law, the Fg of block = Fg of water pushed away. - Since a smaller volume of water has equal mass (and so Fg) to block, and ice is less dense than water, when it melts, no mass is lost, so it will take in less space??? Please help me with this point of thinking. Given two points (defined, for instance using nodes), I want to compute the distance between them.   Is there some build in functionality in tikz to do this? If not, how can it be done using the mathematical engine?   The application I have in mind is to draw an circular arc centered at (a) and passing through some second point (b), where only (a) and (b) are known. Install Ubuntu from ISO image directly from hard disk of a system running Linux? XGBoost Loss function Approximation With Taylor Expansion Daily Ubuntu base update I am getting Ubuntu base update almost every day. This seems strange to me. What am I missing?   (I am using Ubuntu 14.04 LTS) How do I troubleshoot high 'svchost.exe' usage in Windows 7? Proof of Archimedes Principle Say I have an arbitrary body $\Omega$ and surface $\partial \Omega$ submerged in a hydrostatic fluid of density $\rho$ under the influence of gravity. How does one show ? i.e.  $$\int_{\partial \Omega}(P_0 + \rho g h)d\vec{S}=\text{vol}(\Omega)\rho g\vec{e_2}.$$ Papers published from an academic project (MSc or PhD) usually have two authors; the first author is the student who mainly conducted the research, and the second author is the professor who supervised the projects.  The corresponding author is the one who take the responsibility of a paper, and thus, some believe that students are not yet prepared to take this responsibility.  Ideally, who should be corresponding author for papers published by MSc or PhD projects?  I understand that it mainly depends on personal agreements and preferences, but I want to know which case is more reasonable from academic logic? The  makes use of the term "the author."  When Bob makes a post, it's obvious Bob "owns" the content, but what happens when he checks the Community Wiki button? Does it become the property of the Stack Overflow community? Even if Bob is the only one to have edited it?  Say I were to use a Community Wiki answer for something or other &#8212; say, in a book &#8212; who would I attribute the content to? Why won't my computer go to sleep automatically? Windows 8 is set to sleep after 30 mins, and it used to work, but recently it's started refusing to sleep. (I can still manually ask it to go to sleep without any issue.)    I was having issues a while ago, but it was with my network adapter. That's since been disabled, so it's definitely not that:    I've checked to see what devices are able to wake up my machine, but it only appears to be my mouse:    Which is odd, because I haven't recently changed my mouse, and more confusing still: The monitor does go to sleep just fine. If it was actually the mouse keeping my system awake, I'm pretty sure the monitor wouldn't go to sleep.  I've checked my Wake Timers, and nothing:    I've also checked my existing requests...  UPDATE: I found something. What to do with it, I don't know...    Note: Even when /requests says that there's "NONE" under every category, my machine still won't sleep(!).    In short: How can I tell what's preventing my computer from Sleeping?    UPDATE: Ok, so I now have a few more pieces of the puzzle. I came back to my computer and it was ASLEEP! Lawks! It seems that the only times it doesn't sleep is if VLC Player is open, even if a video isn't actually playing.  UPDATE UPDATE: Ok, so it won't sleep sometimes when VLC Player ISN'T running, either. Bah! Did the verb “fire a weapon” exist before the actual introduction of firearms on battlefields?  More specifically, does it make sense for a creative work to have archers (or whatever ranged weaponry) be told to “fire!”, when the world they live in has not yet seen firearms?  It seems some kind of an anachronism to me, since before firearms, “fire” would never propel any projectile...  I've seen several movies do it; I can't remember them all, but for instance I verified it in The Lord of the Rings trilogy (left), Kingdom of Heaven (top right), and more recently Frozen (bottom right):    The first two do it several times (with Kingdom of Heaven also using it on ballistae, and The Return of the King even having Aragorn ask Legolas to ), whereas firearms never appear on the battlefields they feature (Kingdom of Heaven is set in the 12th century; as for The Lord of the Rings, apart from one occurrence of a witchcraft-ish bomb, it's archery and medieval siege engines all the way).  Frozen may be debatable, happening probably somewhere in the 18th or 19th century, but since we only see swords, spears and the like, it made me flinch to hear crossbowmen use “fire!”.  I've also noticed other movies avoiding this, using “loose!” instead, such as Troy (left) and Gladiator (right):    This makes me think it would be the right thing to say instead... although I'm still wondering why not use “shoot”, which seems simpler to me. I'm trying to do something similar to this epsilon-delta graph I've found.  Specifically, I'd like to copy the placements and arrows, like the L+e and L-e coming out of L. Same thing with the x0 + d and x0-d coming out of the x0. Can someone help me with this? This is what I have so far.    \begin{tikzpicture} \begin{axis}[ ,         legend pos=north east,         axis x line=middle,         axis y line=middle,         x tick label style={/pgf/number format/fixed,                             /pgf/number format/fixed zerofill,                             /pgf/number format/precision=1},         y tick label style={/pgf/number format/fixed,                             /pgf/number format/fixed zerofill,                             /pgf/number format/precision=1},         grid = major,         width=8cm,           height=6cm,         grid style={dashed, gray!30},         xmin=0   ,     % start the diagram at this x-coordinate         xmax= 4,    % end   the diagram at this x-coordinate         ymin= 0,     % start the diagram at this y-coordinate         ymax= 11,   % end   the diagram at this y-coordinate %axis background/.style={fill=white},         xlabel=$x$,         ylabel=$f(x)$,         tick align=outside,         enlargelimits=false] % plot the stirling-formulae %\addplot[domain=0:200, red, ultra thick,samples=100] {K/(1 +    ((K-X0)/X0) * exp(r*x))    }; \addplot[domain=0:200, red, ultra thick,samples=100] {3*x-1 };  \addplot[line width=1pt, dashed, mark=none, black] coordinates {(0,8) (3,8)}; \addplot[line width=1pt, dashed, mark=none, black] coordinates {(3,0) (3,8)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(3.33,0) (3.333,9)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(2.666,7) (2.666,0)}; \addplot[line width=1pt, dashed, mark=none, blue] coordinates {(2.666,7) (0,7)}; \addplot[line width=1pt, solid, mark=none, blue] coordinates {(3.333,9) (0,9)}; \addplot[holdot] coordinates{(60,8.66)};  % 1\addlegendentry{$f(x) = 10 \sin (x)$}  \end{axis}   \end{tikzpicture}   which gives Additional Boxes - Criteria, Longevity, Manipulability This feature has existed for a while (I'm not sure since when exactly), but I'm mainly interested in the Gen VI implementation (hence the tag).  Usually, at the start of a game, you have some number of Boxes available. In B/W, those were 8, in X/Y I think it was 15. Under certain conditions though, you receive additional Boxes that just appear at the end of your current Boxes list. Which brings me to Part 1 of my question:     1) What are the exact conditions for additional Boxes to appear and do you always get 8 additional Boxes? (Using Pokemon Bank reveals that in X/Y, the maximum number of Boxes is 31, which I have experienced to be unlocked in 2 steps of 8 Boxes each.)   Since I'm a person who really likes to order and organize stuff, my Boxes have names and are used to categorize my Pokemon. This results in some Boxes ending up empty for a while most of the time. So here's to     2) Do additional Boxes you receive stay forever or do they disappear if the conditions for them are no longer met?      3) If they disappear, is there a way (such as renaming or putting any Pokemon in the last Box) to make them stay no matter what, even if you released all your other Pokemon? Lightning component quick action - send parameters to the lightning component I have a lightning component that is available for use as lightning component quick action. I need to use this component from various object actions, for example, I will add a lightning component quick action to account object and to contact object. Now on the lightning component itself, I want to know if it was invoked from the account object or from the contact object, but I cannot find a way to do that. I have found a way to get the record Id by adding &lt;aura:attribute name=&quot;recordId&quot; type=&quot;String&quot; /&gt; (see code snippet below) It is working but not good enough. What I really need is to send a parameter from the lightning component quick action invocation:  And get it in my component: &lt;aura:component implements=&quot;force:lightningQuickAction,force:hasRecordId,flexipage:availableForAllPageTypes&quot;&gt;     &lt;aura:attribute name=&quot;recordId&quot; type=&quot;String&quot; /&gt;     &lt;aura:attribute name=&quot;param&quot; type=&quot;String&quot;/&gt; &lt;/aura:component&gt;  Is this possible? And if not - any workaround for achieving that? I installed a mainline kernel for testing purposes. I would like to set grub to boot from the older kernel by default.  I know I can set the GRUB_DEFAULT=0 setting for the first page of grub but how do I set it to boot by default from one kernel in the second page (Advanced page)?  I would prefer doing this without installing other software (ex. grub-customizer).     Related Questions: