can't activate rake (= 0.9.2.2, runtime) for [], already activated rake-10.0.2 for []
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What do two question marks together mean in C#? Ran across this line of code:  FormsAuth = formsAuth ?? new FormsAuthenticationWrapper();   What do the two question marks mean, is it some kind of ternary operator? It's hard to look up in Google. There are various articles on Hearthstone opening strategy which suggest it's a bad idea to use early-game spells and summons to damage your opponent directly, and that you should instead save them for minion removal.  An example: your starting hand contains an Elven Archer, a 1-cost 1/1 minion that does a point of damage when summoned. I've seen it advised that if going first, with that card in your hand, you should not play it, but save it for minion removal.  Another example:  Going second against a Rogue with a 2-cost 2/1 Loot Hoarder, Deathrattle: draw a card in your hand. The advice was not to play it and save the coin, because on her second turn, the Rogue can generate a dagger and kill the Hoarder.   I understand why, in most circumstances, it's better to remove a minion than damage the enemy. What's bugging me about these particular opening examples is why they're a better idea than doing nothing and ending the turn.  In both cases, you've wasted a point of mana, and the chance to take the initiatve. By having a minion on the board first, you can use the following turn to attack with that minion, possibly removing an enemy summon and leaving you clear to summon onto an empty board.   The Loot Hoarder one I find particularly puzzling. If the Rogue gets a dagger and kills it, you still have the initative, you've forced the Rogue to make what's possibly a suboptimal turn-2 play, you've done 2 damage to the Rogue and you got a card into the bargain. Sounds like a pretty good use of the coin to me.  What am I missing here? How can I tell whether beetroot is still edible? I have some raw beetroot I bought about a week ago, having stored them at room temperature since. It's the first time I bought it raw, and I'm unsure whether it's still edible.   It is already soft, and when I cut it, it smells... Well, different than I expected. It's not a rotten smell as such, but it's nothing like the sweet beet-rooty smell I know from the pre-packaged, pre-boiled supermarket variety.  How can I tell whether it's still safe to eat? I want to know how to get the X and Y position of HTML elements such as img and div in JavaScript relative to the browser window. Lifting idempotents modulo a nilpotent ideal The problem is this:      Suppose $I \subseteq R$ is a nilpotent ideal and there is $r \in R$ with $r \equiv r^2 \pmod I$. Show $r \equiv e \pmod I$ for some $e \in R$ idempotent.   I have spent a few hours rolling around in abstracta with no destination. I believe that if I could write down a concrete example of this, the example could guide me through the abstract definitions and show me where to look for an idempotent in $R$. I have looked at 2x2 matrices and could not find any such examples. Might anybody have one? Selectively coloring text in RichTextBox How can I paint in red every time I meet the letter "A" in RichTextBox? How to enable bullet points when using the presento beamer theme? I have the problem that when I use an itemize list and the , there are no bullet points.  Here is a minimal working example (requires the  not available on CTAN to be downloaded first):  \documentclass{beamer} \usepackage{config/presento} \begin{document} \begin{frame} \begin{itemize} \item ... \item ... \item ... \end{itemize} \end{frame} \end{document}     How to fix this problem? How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number? I was looking at the Fibonacci sequence:  $$1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,\ldots, F_n : F_n + F_{n - 1} = F_{n + 1} \land F_0 = 0$$  Here I noticed something; $\qquad F_n^2 + F_{n\pm1}^2 = F_{2n\pm1} : n\in \mathbb{N}$  For example; $$\ \ F_3^2 + F_{3 + 1}^2 = F_3^2 + F_4^2 = 2^2 + 3^2 = F_{2\times3 + 1} = F_{6 + 1} = F_7 = 13$$ $$F_3^2 + F_{3 - 1} = F_3^2 + F_2^2 = 2^2 + 1^2 = F_{2\times3 - 1} = F_{6 - 1} = F_5 = 5$$ However, no matter how true this can seem, I cannot seem to prove/disprove it.    My Attempt: $$\because (a + b)^2 = (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + b^2 + 2ab : (a,b)\in \mathbb{Z}$$ $$\implies F_n^2 + F_{n\pm 1}^2 = (F_n + F_{n\pm 1})^2 - 2F_nF_{n\pm 1}$$ $$\implies F_n^2 + F_{n - 1}^2 = F_{n + 1}^2 - 2F_nF_{n - 1} : F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_n^2 + F_{n + 1}^2 = F_{n + 2}^2 - 2F_nF_{n + 1} : F_n + F_{n + 1} = F_{n + 2} \iff F_n + F_{n - 1} = F_{n + 1}$$ $$\implies F_{2n\pm 1} + 2F_nF_{n\pm 1} = F_{n + 2\lor1}^2 : F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1} \tag{+2 if +, +1 if -}$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1} - F_{n\pm 1}^2}\sqrt{F_{2n\pm 1} - F_n^2}= F_{n + 2\lor1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{(F_{2n\pm 1} - F_{n\pm 1}^2)(F_{2n\pm 1} - F_n^2)} = F_{n + 2\lor1}^2$$ $$\implies F_{2n\pm 1} + 2\sqrt{F_{2n\pm 1}(F_{2n\pm 1} - F_n^2 - F_{n\pm 1}^2) - (F_nF_{n\pm 1})^2} = F_{n + 2\lor1}^2$$.  $$\because F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$$ $$\implies F_{2n\pm 1} + 2\sqrt{-(F_nF_{n\pm 1})^2} = F_{n + 2\lor1} \neq F_{2n\pm 1} + 2\sqrt{\big(-(F_nF_{n\pm 1})\big)^2}$$ $$\therefore F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} : i = \sqrt{-1}$$  I have looked over every step and cannot see where I am wrong. The only part that must be wrong is that:  $$F_{2n\pm 1} + 2F_nF_{n\pm 1}i = F_{n + 2\lor1} \iff F_n^2 + F_{n\pm1}^2 = F_{2n\pm 1}$$  I can seperate $F_{2n\pm 1}$ as $F_n^2 + F_{n\pm 1}^2$ (if true) so I turn the equation into:  $$F_n^2 + F_{n\pm 1}^2 + 2F_nF_{n\pm 1}i = F_{n + 2\lor1}$$ $$\therefore (F_n + F_{n\pm 1})\bigg(\frac{F_n}{F_{n\pm 1}} + \frac{F_{n\pm 1}}{F_n} + 2i\bigg) = F_{n + 2\lor1}$$ Now I know that the greater the value of $n$, one of the fractions in the above equation (depending on which sign is used in $F_{n\pm 1}$) will get closer to the golden ratio $φ = \frac{1 + \sqrt{5}}{2}$ but $i = \sqrt{-1}$ is not a "real" number, although $F_n$ is.  I then searched for other formulae for finding $F_n$ and came across the one below (being Binet's Formula):  $$F_n = \bigg\{\frac{φ^n - ψ^n}{φ - ψ} : ψ = φ - \frac{\sqrt{20}}{2} = \frac{1 - \sqrt{5}}{2} \ \land \ φ - ψ = \sqrt{5}\bigg\}$$  But I do not know what how to turn that into $F_{n\pm 1}$. Could you please show me where I went wrong (because I must have gone wrong somewhere), and also if you wish, could you please show me how to turn the above fraction into $F_{n\pm 1}$ (if possible).  I only used the $(a + b)^2$ expansion rule because my skill level in mathematics is not particularly high compared to most of the users on this site (especially when logging into the MSE and finding fancy symbols like $\nabla$ and $\partial$ and $\sum$ which all look Greek to me, however the only "fancy" thing I know is that $i = i^5 = \cdots = \sqrt{-1}$) so if you used any other techniques in trying to prove this formula, could you please show me step by step?  Much appreciated. Thank you in advance.    Edit: I believe this question is a duplicate of this other question $\longrightarrow$   and I can go here to serve as a little hint $\longrightarrow$ Reference to the Table of Contents page I thought that someone must have asked this, but my searches didn't find it.  I am looking to refer back to the table of contents from places in my document. How can I do this? How to achieve a super leavened cake as the Pierre Herme ones? I made several cakes in my life. I know the difference between different leavening agents. I know that low temperature tends to make flatter cakes, but I never could get this kind of shape. If I use a super hot oven I burn the surface and I don't get this shape, there must be something else. Does anyone have experience doing this? Does anyone have a recipe from any modern pastry chef showing this kind of cake? Maybe gluten content in the flour could help?  Thank you We are developing a new Lightning Community to replace our Partner Community. However, when we use our visualforce pages with LightningStylesheets=true on the Lightning Community, the Lightning styling is not applied.  I understand that this is the case because Lightning Communities are not Lightning Experience.  Is there a way to force LightningStylesheets anyway? I am trying to stay away from having to rebuild/restyle all our legacy visualforce pages. Experimental Fractional scaling makes fonts dirty in Ubuntu 17.10 I updated to 17.10 from 17.04.   I activated the fractional scaling by running the following command.   gsettings set org.gnome.mutter experimental-features "['scale-monitor-framebuffer']"   Then, I changed 125% scale. The scale was changed, but the fonts and icons are so dirty.    The launcher icon and font in Google Chrome and other application except the system setting are dirty.  How can I resolve this problem?  For some reason, font in the system setting is not dirty... Why doesn't 'find' show this file? Using find with grep, one can locate files that match a pattern:  # find | grep error ./solr-modifiedSolr4/SolrPhpClient/phpdocs/errors.html ./error_log ./includes/classes/error_log   However, using find alone the first file is not found:  # find . -name error* ./error_log ./includes/classes/error_log   Why doesn't find locate the errors.html file when not used with grep? How is find used to show this file as well? Tractatus 3.333 and Russell's paradox Can anyone explain to a non-logician how Tractatus 3.333 refutes (or fails to refute) Russell's Paradox? Please explain his use of symbols! I have a question about using the phrase "some kind of _".  Is it incorrect to say "some kind of + plural noun"?     For example, is it wrong to say "are these rock-like things some kind of chocolates?"   I didn't use "kinds" and that kind of adds to my question. Is "kind" always plural, like "some kinds of chocolates"? Because although I'm using "some", it feels like "kind" shouldn't be a countable noun.  Anyway, I don't think I've heard of "some kind of + plural", but I think it makes more sense then using singular, since I think chocolates are countable. Please help! I made a bootable Windows 7 USB using UNetbootin, and when I try to boot from the bootable USB and select the Default boot menu entry, it gets stuck at the UNetbootin boot menu and it keeps repeating an Automatic boot in 10 seconds... message in an endless countdown loop. Selecting Press [Tab] to edit options and editing the options has no effect. When I go back to the boot menu, it keeps repeating the same countdown loop.   I've tried redoing the UNetbootin extraction, but I still have the same issue. Frequent Write to Non-volatile Memory Will Determinism be ever possible? g++ undefined reference with a shared library Is it possible to search for down voted questions?