Is it safe to upgrade Windows version with Ubuntu installed alongside?
How do I install Ubuntu alongside a pre-installed Windows with UEFI?
Update help center on syntax highlighting to point to an actual list of options Reading the help center article on syntax highlighting, one of the paragraphs within it reads:     You can use either , like lang-cpp or lang-sql, or you can specify a tag, and the syntax highlighting language associated with this tag will be used:   Note the link in there, which goes to .  Problem is, a long time ago we removed the list of options from several questions/answers across meta Stack Exchange because it was a pain trying to keep all of them updated. It makes a lot more sense to just have one list that we keep updated, and the most logical place for that list was in the , which is where it now resides.  Can the link in the help center be updated to point directly to the list, rather than to a post that explains that the list has been moved? Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$ I can't figure out an algebraic proof for the following identity:  $$\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$$  Combinatorical solution:  We can see that as choosing some from $n$ and the rest of $k$ from $m$, thus $k$ in total.  Or we could just choose $k$ from the union. I've tried to setup an autologin, but that isn't possible, because my home is encrypted. What are the reasons for this?  PS. Here I have described my problem: . How do I easily rename multiple files using command line? What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? It has been a long time since I have used calculus, and I am trying to understand how the mean and variance of the Laplace distribution with pdf $$f(x|\mu,\sigma) = \dfrac{1}{2 \sigma}\,e^{-\Large\frac{|x-\mu |}\sigma}$$ are derived.  I know that E$[X] = \mu$ and Var$[X] = 2\sigma^2$, but I don't understand how that happens.   Many thanks. Lightning force:createRecord capture redirect after save Is there a way to use force:createRecord but capture the redirect to the newly created record page that occurs after saving the record? Finally, prevent the redirect from completing?  createRecord : function (component) {     var createRecordEvent = $A.get("e.force:createRecord");     createRecordEvent.setParams({         "entityApiName": "Event__c"     });     createRecordEvent.fire(); } Zorn's Lemma states that if every chain $C$ in a partially ordered set $X$ has an upper bound then there is at least one maximal element in $X$.  Let $n\in \mathbb{N}$, $C_n \subset \mathbb{N}$ be the set containing the natural numbers $\{1,\dots,n\}$. Then if $k\le n$, $C_k\subset C_n$, so $C_n$ is a chain. Also, $C_n$ has an upper bound, such as $n+1$. But what is the maximal element of $\mathbb{N}$?  There's something I don't get in Zorn's Lemma statement. Could someone please tell me what the symbol ringed in red represents?     I know it has ON Switch pointing to it, but the symbol has other lables in different parts of the document. How many questions on meta have asked, "Why can't I ask this question when that question is open"? How can I model the mechanics of an army battlefield scene? TL;DR;  I want to model a strategic battlefield fight for my players to command and participate. I'm seeking advice on how to model it mechanically so that it is exciting for the players.  Background  The final scene of Act II of my campaign is envisioned to be a big battle between the army of the Big Bad and the allied forces gathered by my players. The full set of Act II runs with the players gaining the allegiance of the different factions to support them on the fight.  Now, in terms of that final scene, I'm struggling to decide how to DM the fight. In games and movies the action is made epic by having cinematic scenes of the fight happening with cuts to our heroes doing their amazing things, be it just plowing through dozens of enemies in quick succession or fighting the big ugly overpowered monster that is otherwise cause havoc among the army. I want that feeling  The set up will involve an army of several thousand enemies agains the different forces gathered by my players. Depending on what they've done during the second act, they'll have more or less support with a minimum number of regiments belonging to several faction (i.e. the silver guard of Wizardwight).  Intended way of DMing the scenario.  What I've come up with is to have the players be military leaders. Draw the map of the battlefield and have them manage the battlefield strategically and tactically, distributing the units and, somehow, enabling a dice based mechanism to evaluate how well each unit is doing. This will transform the tabletop into something similar to Warhammer Fantasy. They can choose to join a particular place of the battlefield to help either together or separately.  I have absolutely no idea on how to model this mechanically (as far as I know D&amp;D 5e does not cover this kind of fights).  Question:  What are good ways to mechanically model this kind of strategic army combat? Should I switch to a different system just for this scene or can I model this with D&amp;D 5e?  Notes on level: At this point I expect my players to range between level 9-12 and for the party to be between 3 and 4 players (this is not a limitation of the campaign, more like the players I'm running the campaign with). $\exp(A)$ is orthogonal iff $A$ is skew symmetric Let $A \in M_n(\mathbb R)$ and $\exp(A)=\sum_{i=0}^{\infty}\frac{A^i}{i!}$. How to prove $\exp(A)$ is an orthogonal matrix iff $A^t=-A$?  I can get that $\exp(A)$ is an orthogonal matrix iff $\exp(A^t)=\exp(-A)$, but how to get $A^t=-A$ from it?  What's more, is $\exp(A)$ injective or not? Error installing any module Ubuntu gets stuck in a login loop My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M How do you post to an iframe? How do you post data to an iframe? Showing that the class of all sets of a particular cardinality is not a set. How to show that the class of all sets of a particular cardinality ,say $h$ is not a set.   My argument:  I assume that I've shown the following lemma.  Lemma: If $X$ is an infinite set of cardinality $h$ , $a\ne x$ for every $x\in X$ then $\{a\}\cup X$ is of cardinality $h$ too i.e. adding new element to an infinite set doesn't change cardinality.  Let $h$ be an infinite cardinal number. Let $T_h=\{x:\text{x is a set of cardinality h}\}$. Suppose $T_h$ is a set.   Let $a$ be any set and consider any $t\in T_h$. Let $R=t\cup \{a\}$. Using the above lemma, $R\in T_h$.   So, $a\in R\subset \bigcup T_h$. As $T_h$ is a set then $\bigcup T_h$ is also a set.  As $a$ was arbitrary set then we have, $a\in\bigcup T_h$ for every set $a$. Hence, the set $\bigcup T_h$ contains all sets which meas that the collection of all sets is a set, contradiction.    If $h$ is non-zero finite cardinal number. Define $T_h$ the same way as above. Let $a$ be any set, Let $A_1=a, A_{n+1}=A_n\times a$. Consider $A=\{A_1,A_2,...,A_h\}$. So, $A\in T_k$. Hence, $a=A_1\in \bigcup T_h=K$. So K is a set containing all sets $a$ since $a$ was arbitary,contradiction.  My main question is, Is there any flaws in my argument? If yes, point it out please.   If the argument is valid, Is there any standard proof to show the same fact? Apply the latest Service Pack and Cumulative Update What are the rules for China's visa-free transit programs? Assuming one wants to travel through China, what are the rules for visa-free access? To be more specific:   How does the 24-hour visa free transit work? How does the 72-hour version work? What does a person ineligible for either of these programs have to do to transit China? Do the programs apply to flights only or do they also work for transit on land? Would a visitor save much hassle by using visa free transit instead of just getting a visa?      NB: this is intended as a canonical question on transiting China Almost sure convergence of the Poisson process Let $N = \{N(t) \}_{t\geq 0 }$ be a Poisson process. I already know that $N(t)- \lambda t$ is a martingale where $\mathbb{E} [ N(t) ] = \lambda t$.   I want to prove that $$ \frac{N(t)}{t} \rightarrow \lambda, \quad t \rightarrow \infty \quad \text{ a.s.}. $$  To prove this I received a hint that I should use the martingale law of large numbers which states that:  Theorem: (Martingale LLN)  Let $S= (S_n = \sum_{k=1}^n X_k)_{n=1,2,\ldots}$ be a martingale with respect to the filtration $(\mathcal{F}_n)_{n=1,2,\ldots}$. Then $\sum_{k=1}^n X_k/k$ converges almost surely on the set $\left\{ \sum_{k=1}^\infty k^{-2} \mathbb{E}\left[ X_k^2 \mid \mathcal{F}_{k-1} \right] &lt; \infty \right\}$. Hence $S_n/n \rightarrow 0$ a.s. on the same set.  Now to use this theorem I think I need to use Doob-Meyer to decompose $N(t)$ as the sum of a martingale and an increasing process. Which would be the martingale $M(t) = N(t) - \lambda t$ and increasing process $A(t) = \lambda t$. But how is $M(t)$ the sum of a martingale? And I do not know how this exactly relates to the thing I have to prove. Thanks for any help. I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support. &lt;body&gt;     &lt;div&gt;Div to be aligned vertically&lt;/div&gt; &lt;/body&gt;  How can I center a div vertically in all major browsers, including Internet Explorer 6?