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Number of functions from n-element set to {1, 2, …, m} I've gotten stuck at the following exercise;     There are m functions from a one-element set to the set {1, 2, …, m}.   How many functions are there from a two-element set to {1, 2, …, m}?   From a three-element set? Give a recurrence for the number of T(n) of   functions from an n-element set to {1, 2, …, m}. Solve the recurrence.   I'm not sure how to begin solving it? How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and . XML to CSV Using XSLT I have the following XML document:  &lt;projects&gt;   &lt;project&gt;    &lt;name&gt;Shockwave&lt;/name&gt;     &lt;language&gt;Ruby&lt;/language&gt;     &lt;owner&gt;Brian May&lt;/owner&gt;     &lt;state&gt;New&lt;/state&gt;     &lt;startDate&gt;31/10/2008 0:00:00&lt;/startDate&gt;    &lt;/project&gt;   &lt;project&gt;    &lt;name&gt;Other&lt;/name&gt;     &lt;language&gt;Erlang&lt;/language&gt;     &lt;owner&gt;Takashi Miike&lt;/owner&gt;     &lt;state&gt; Canceled &lt;/state&gt;     &lt;startDate&gt;07/11/2008 0:00:00&lt;/startDate&gt;    &lt;/project&gt; ...   And I'd like to get this from the transformation (XSLT) result:  Shockwave,Ruby,Brian May,New,31/10/2008 0:00:00 Other,Erlang,Takashi Miike,Cancelled,07/11/2008 0:00:00   Does anyone know the XSLT to achieve this? I'm using .net in case that matters. How can I update all Snap packages? I know that I can update a snap package using  sudo snap refresh &lt;package&gt;   But is there a way to update all snaps, like   sudo apt dist-upgrade Non-hidden directory doesn't show in Explorer, but the program that made it can access it What happened to Control.InvokeRequired in WPF? Generate the smallest $\sigma$-algebra containing a given family of sets My teacher gave me an example of performing the subject:     Example      Let $\Omega = \Bbb R$ and $\mathcal R = \{(-\infty,-1),(1,+\infty)\}$.   Then $\sigma(\mathcal R) = \{\emptyset, \Bbb R, (-\infty,-1),  (1,+\infty), [-1, \infty), (-\infty,1],  (-\infty,-1)\cup(1,+\infty),[-1,1]\}$.   There was a different example, where she also generated the smallest  $\sigma$-algebra for the family of sets $\mathcal A = \{A,B\} \subset 2^\Omega$ in the same way: $\sigma(\mathcal R) =  \{\emptyset, \Omega, A, B, A^C,B^C,A\cup B, (A\cup B)^C\}$.   I certainly understand why $\emptyset$, $\Omega $ and a family of sets itself are there, and I certainly know that $\sigma$-algebra is closed under the operations of complement and union. What I don't understand about the other elements of generated $\sigma$-algebras: why we are taking exactly them? Does this work in a general case? When is "seems to be" used instead of "seems"? The baby seems happy/comfortable. The baby seems to be happy/comfortable.   Are these both correct? If both are correct, what are the differences between them? Generating list of manually installed packages and querying individual packages What is the metal sheath surrounding a USB connector, and is it commonly connected? What circumstances can cause a question or answer to be deleted, and what does that actually mean?    How can a post be deleted? When can't I delete my own post? Can I still see my post even after it's deleted? Can I see a list of my deleted posts? How can I undelete one of my posts? What does deletion mean for a post? How do votes to delete work? What are the criteria for deletion? What else should I know about deleted posts? If I flag my question with a request to delete it, what will happen?       For more information, see the articles about  and  in the . Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A In the next proof we avail ourselves of the next lemma: For all sets A and B, ( A ∪ B ) - B = A. Proof: Let A and B be arbitrary sets and let x ∈ ( A ∪ B ) - B. x ∈ ( A ∪ B ) - B ⇔ x ∈ ( A ∪ B ) ∧ x ∉ B ⇔ ( x ∈ A ∨ x ∈ B ) ∧ x ∉ B ⇔ ( x ∈ A ∧ x ∉ B ) ∨ ( x ∈ B ∨ x ∉ B) For p ∧ ~ p ≡ F and p ∧ q ⇒ p where p and q are prepositions, ( x ∈ A ∧ x ∉ B ) ∨ ( x ∈ B ∨ x ∉ B ) ⇔ x ∈ A ∨ F By modus tollendo ponens, x ∈ A ∨ F ⇔ x ∈ A So then, x ∈ ( A ∪ B ) - B ⇔ x ∈ A And ( A ∪ B ) - B = A Therefore, the statement for all sets A and B, A ∩ B = ∅  implies ( A ∪ B ) - B = A is true trivially. Is this proof right? Doubt regarding a limit which is related to MVT Let the function $f(x)$ be differentiable  and $f'(x)$ be continuous in $\left(-\infty,\infty \right)$ with $f'(2)=14$ then evaluate the limit  $$\lim_{x\to 0}\frac{f(2+\sin x)-f(2+x\cos x)}{x-\sin x}$$  My attempt:  $\lim_{x\to 0}\frac{f(2+\sin x)-f(2+x\cos x)}{x-\sin x}$  $\lim_{x\to 0}\left(\frac{f(2+\sin x)-f(2+x\cos x)}{\sin x-x\cos x}\right)$ $\frac{\sin x-x\cos x}{x-\sin x}$$=\left(f'(2)\right)(2)=28$  Is the method used here correct What does rate of change actually mean? If we have a function, say, $y=x^2$, then $dy/dx=2x$. Now $y=1,4,9,16...$ for $x=1,2,3,4...$ and $dy/dx=2,4,6,8...$ for $x=1,2,3,4...$ Now as $dy/dx$ represents rate of change of y w.r.t x but I can't understand how these particluar values of $dy/dx$ represent change ? I mean for x=3, the rate of change is 6. What does it mean ? My group of 8 level 3 players are about to run through the Thundertree Ruins and will probably have a hand at fighting the dragon. My question stems from the fact that a single poison breath attack from the dragon will outright kill all but 1 player assuming they fail their saving throws.  I understand this encounter is supposed to be ridiculously deadly, but I don't want to be punishing my players for testing the lengths at which they can fight stuff. A fight should be challenging and they should be able to try and run away, but instant obliteration seems a bit much.  All PCs are level 3 (HP in parenthesis):   Wood elf moon druid  (27) dwarven frenzy barbarian (44) fire genasi archer ranger (37) (pseudodragon companion (12)) wood elf assassin rogue (27) human wild magic sorcerer (22) dragonborn fighter (29) human monk (24) human fighter (32) I have created two files:  sample.txt and sample.txt  (the second file contains some hidden characters, e.g. a space). How can I remove the latest modified file? I'm using Linux. I want Ctrl+Alt+B bring up a browser.  Ctrl+Alt+Delete is handy.  Can I set up Ctrl+Alt+B to bring up a browser (either default or specific)? I'm looking to schedule 16 players to play a round robin tournament with each other such that there are 4 players at each table.  I'd like for each player to play with each other player exactly once over the course of 5 rounds.  I just took a look at this post:  , and I was wondering if anyone knows if the case n=m=4 has been solved, and if so what that solution is. Singular values of the data matrix and eigenvalues of the covariance matrix Check which IPs or web-sites an app is communicating with? Usually they do it behind the scenes. So I'd love to know where apps are actually sending data and from whom they are actually getting responses.