What am I doing Wrong here
How do I compare strings in Java?
How can we show that the following sequence converges? $(a_n)$ is a bounded sequence with the following condition  $a_{n+1}\geq a_n-\frac{1}{2^n}$   The sequence converges, but how do we show it? What's the regular expression that matches a square bracket? I want to have a page-filling and -breaking longtable, so I decided to try xltabular. Unfortunately xltabular seems to screw up the booktabs rules in the normal tabular environments, see:  \documentclass{article} \usepackage{booktabs, xltabular} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tabular} \begin{document} \begin{tabular}{ccc}     \toprule     col1 &amp; col2 &amp; col3 \\     \midrule     row 2: &amp; more and moooooooooooore &amp; test \\     \bottomrule \end{tabular} \end{document}     Not loading xltabular resolves the issue.  Did I miss some package option or some incompatibilities? Is there a better package than xltabular which doesn't break booktabs?  (I am using TeXLive 2019 and compile with lualatex)    EDIT (by Skillmon)  I reduced the bug to the following MWE (which doesn't make much sense on its own), it looks like booktabs tries to be smart detecting something, but fails badly.  \documentclass{article} \usepackage{longtable} \let\xltabular\relax \usepackage{booktabs}  \begin{document} \begin{tabular}{ccc}     \toprule     col1 &amp; col2 &amp; col3 \\     \midrule     row 2: &amp; more and moooooooooooore &amp; test \\     \bottomrule \end{tabular} \end{document}   It seems to suffice that longtable is loaded and \xltabular is defined (even if it's just \relax). If you cast Polymorph on a non beast creature then cast Awaken on their beast form how much carries over after polymorph ends?  Polymorph does not give any explicit information on what happens to your statistics when the polymorph ends:     The transformation lasts for the duration, or [drops to 0 hp]. [...] The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.  (Basic Rules, pg. 266)   So this leaves ambiguity when game statistics are altered during polymorph,   The charm effect of Awaken seems pretty clear from the  and reinforced by the specific wording referring to the target as a beast or plant during effects and a creature afterwards:     The awakened beast or plant is charmed by you [longer than polymorph.] When the charmed condition ends, the awakened creature chooses [...] (Basic Rules, pg. 216)   The other two effects of awakening (other than making a plant mobile) are less clear-cut:     The target gains an Intelligence of 10. The target also gains the ability to speak one language you know.  (Basic Rules, pg. 216)   I would guess the modification to intelligence would apply to the beast's stats and therefore end with polymorph.     as being independent of creature statistics and act more as the character's experience. I'd argue the experience of a stranger turning you into a mouse, then gifting you the ability - as a mouse - to speak a language you have never used before would be an experience you couldn't lose I'm not sure if the language and intelligence granted from awakening should remain linked.    These are two examples I can see this having significant impact on my campaign:   Meet an NPC I don't share a language with, Polymorph them then Awaken their beast form so they can speak my language. Can I now communicate with them when they turn back?  If their original intelligence was higher then 10 is it reduced to 10? Say I use find familiar to get an owl (classified as a fey) familiar, then polymorph it to an owl (classified as a beast) so my druid friend can cast Awaken on it, does my familiar keep an intelligence of 10 and/or the ability to speak?   So after reverting from an awoken polymorphed state would you keep the 10 intelligence and a new language, only the new language, or not keep either? If $|A| > \frac{|G|}{2} $ then $AA = G $ I'v found this proposition.  If $G$ is a finite  group , $ A \subset G $ a subset and $|A| &gt; \frac{|G|}{2} $ then $AA = G $.  Why this is true ? If $f^2$ is an analytic function then so is $f$ I want to show the following:  If $f(z) $ is a continuous  function on a connected open subset of the complex plane and $f(z)^2$ is an analytic function, then $f(z)$ is analytic.  Clearly if $f(z) \neq 0$ then $$\frac{f(z+h)-f(z)}{h}=\frac{f(z+h)^2-f(z)^2}{h}.\frac{1}{f(z+h)+f(z)}$$  which shows $f^\prime(z) $ exists if $f(z)\neq0$.  What do I do when $f(z) =0$? Get Absolute Position of element within the window in wpf I would like to get the absolute position of an element in relation to the window/root element when it is double clicked. The element's relative position within it's parent is all I can seem to get to, and what I'm trying to get to is the point relative to the window.  I've seen solutions of how to get a the point of an element on the screen, but not in the window. redraw GUI on didreceivelocalnotification when come from lock screen iphone Why is wine made 'from' grapes, but tables are made 'of' wood? (1) Wine is an alcoholic beverage made from fermented grapes or other fruits. (Wikipedia) (2) Tables were made of marble or wood and metal (typically bronze or silver alloys), sometimes with richly ornate legs. (Wikipedia)  Why is 'from' used in (1), whereas 'of' is used  in (2)? Is it a stylistic choice whether to use 'of' or 'from'? Or, in case of chemical changing, differently from changing in shape only, 'from' is preferable? Stack Overflow is getting a Meta of its own What was the Historical Precursor for .NET Attributes? What languages or platforms influenced the .NET 1.0 Team to build-in the concept of Attributes from the very start? Was this an Aspect-Oriented thing? Serialization? or something else? I was still in VB6-land at this time, and never used any of the pre-1.0 .NET versions. Mouse cursor flickering and disappearing Who invented "dooblidoo"? The word  is used by several different youtube channels as a different word for the youtube description bar. I've seen it used by the  and by .  Who was first to use and invent the term? Choose a default app for opening files with no extension? Is it possible to set a default application to open files with no extension?  I'm not referring to files with hidden extensions, but those completely lacking an extension -- e.g. README, CHANGELOG, mbox, etc.  "Open With" => "Change All" on these files doesn't work, returning the error shown below:    Ideally, I would like the system to try opening all such files in TextMate.  I know I can drag files onto Dock icons to open them in specific apps, but I'm looking for a more seamless solution than that (especially since I have my Dock auto-hide, which makes it much more cumbersome).  I am familiar with the  QuickLook plugin that can enable QuickLook for some of these files, but I would prefer a solution with selecting/copying/editing capabilities. $ KC $ spaces imply $ US $ spaces , but vise versa is false. Does anyone remember this article about the Euclidean Algorithm? In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem? I'm studying orientability of manifolds currently and I'm having trouble to prove the following: $M\times N$ is orientable iff $M$ and $N$ are orientable.   I am able to prove that the product is orientable if components are orientable (chart is $\{(U_\alpha\times V_{\beta},\phi_\alpha\times \psi_\beta):(\alpha,\beta)\in A\times B \}$, and $\det J=\det J_1 \det J_2&gt;0$ by Cauchy-Binet's theorem), but I don't know how to prove the other direction.   So why this holds: if $M\times N$ is orientable, then $M$ and $N$ are orientable?  Thanks in advance. What is the behaviour of \fontsize if baselineskip is below a certain value? during my optimization process I found something spurious I cannot explain to myself and which I would like to understand. So with \fontsize you set the fontsize and the baselineskip. However the behaviour of the second paramater is a bit unclear to me, because if you reduce it too much, at a certain point the baselineskip gets bigger again. Let me show you my example: \documentclass[landscape]{article} \usepackage[margin=1cm]{geometry} \usepackage{lipsum,multicol}  \begin{document} \begin{multicols}{4}     \fontsize{10}{11}\selectfont     \lipsum[1]     \columnbreak          \fontsize{10}{10}\selectfont     \lipsum[1]     \columnbreak          \fontsize{10}{9}\selectfont     \lipsum[1]     \columnbreak          \fontsize{10}{8}\selectfont     \lipsum[1]     \columnbreak \end{multicols} \end{document}  If you compile this, your result will be looking like this:  Now from the first to the third column it seems logic, that the baselineskip is reduced and hence less space is needed vertically to typeset. But with the third column, even though the baselineskip is reduced even further, it needs more vertical space overall. It is strange however, that for example from line 11 to 12 (starting with tus and lum), the spacing seems to be narrower than in column 3, while in a lot of line the spacing is bigger. Changing the baselineskip to lower values down to 0 does not modify the vertical alignment further. What is the purpose of this behaviour and is it intended? I cannot see a benefit of this and I am a bit confused. Speed of object towards a point not in the object's trajectory? What could cause this? f12:    Viewport:    (the f12 has fewer samples, but even when the viewport is at lower samples it looks different..)  I know about color management, but that is at the defaults..    EDIT: oops.. I know 'log' is not a default, but that is because I was fiddling with it. The image above is rendered with 'default'    The material is quite simple, only a translucent shader. (for testing) I even tried appending everything into a new file to reset all the settings, but no difference.  EDIT2: Uploaded blend