Can I use a hand holding a focus from one class to cover somatic components for a spell from another class? I want to try playing a multiclass Hexblade 2 / College of Swords Bard 18, but I'm concerned about how focused will work.  I intend to hold a shield in one hand with a sword in the other. Thanks to College of Swords I am able to use the sword as a focus for my bard spells. However, I was hoping that I would be able to cast Shield from my hexblade spell list in the thick of battle.  As Shield requires a Somatic component, would I be able to use my sword hand (which is holding a focus, but for bard spells not warlock spells) to cover the Somatic components of Shield? I know that if it had a Material component I would need an arcane focus, but this situation seems ambiguous to me.  tl;dr Can I use my hand holding a bardic focus to cover the Somatic components for a Warlock spell?  pg. 15 XGtE under Bonus Proficiencies:     If you're proficient with a simple or martial melee weapon, you can use it as a spellcasting focus for your bard spells.   pg. 203 PHB under Material (M):     A spellcaster must have a hand free to access these components, but it can be the same hand that he or she uses to perform somatic components.   This doesn't actually state that materials are required for you to use the a hand holding the material components to perform somatic components.  I was really just hoping to get a response that cited a rule I might have missed (preferably about multiclassing, but such rules in the PHB skip over foci entirely).
Can a wizard using an arcane focus quarterstaff and a shield still cast somatic component spells? If there is a wizard that, by some means, has acquired proficiency in the use of shields, can said wizard use his shield in one hand and his arcane focus quarterstaff in the other and still cast somatic component spells?  Since the quarterstaff has been crafted to also be an arcane focus, and the Sage Advice Compendium states that you can provide the somatic components of spells with the same hand wielding the arcane focus, in this case an arcane focus quarterstaff, could that wizard still be able to perform somatic component spells while using a shield in the other?  I understand War Caster is the feat that allows you to cast somatic component spells even while using a shield and weapon or two weapons in each hand, but is this a simple way around those rules seeing as this "weapon" is your arcane focus? I would like to believe it is not, but I'm not fully fluent in the ways of spellcasting.
Finite Abelian groups with the same number of elements for all orders are isomorphic Let $A$ and $B$ be finite abelian groups. Suppose that for every natural number $m$, the number of elements of order $m$ in $A$ is equal to the number of elements of order $m$ in $B$. Prove that $A$ and $B$ are isomorphic.  Idea Given that these groups are finite, I think you have to use the primary decomposition theorem somehow. I noticed in this thread the OP successfully managed to connect a 30" cinema display to the new Macbook Pro USB-C, with full resolution:    I have the official Apple dual DVI adapter, going to a displayport > USB-C adapter like yours, however the screen does not fire up.  I then tried a multi adapter instead of the single displayport > USB-C, which worked but only at 1280 resolution:    Would the official Apple Dual DVI adapter not work? On Linux can I keep a program running in background even after I disconnect? If I'm logged into a remote Linux machine, I know I can suspend a process (cntr-z) and move it to the background (bg 1) but if I disconnect from the machine, the process stops.  Is there a way I can leave it in the background and have it there when I log back in? This is a very long running process.  On Ubuntu, logged in via SSH. What are the possible catch bonuses and how much experience do they reward? I found , earlier, and found out that I can throw a curveball at pokémon to earn an increased experience bonus.  I have since noticed two more bonuses: "Great" and "Nice". I had assumed the bonuses were for throwing a pokéball with the 'catch circle' closer to the center, which according to the FAQ, increases the chances of actually catching the pokémon.  However, I have since noticed that the 'catch circle' is actually bigger in cases where I have earned a "Great" bonus. Despite appearing to be a less powerful throw, I earn more experience than when I earn a "Nice" bonus. "Great" nets me 50 experience, while "Nice" only nets 10 experience.  What are the possible catch bonuses, and how much experience do they reward?  For bonus points, every so often I am awarded an additional 10 experience points that are not accounted for on the experience screen. The screen lists my bonuses, and tells me how much experience I have earned, but I am clearly rewarded additional experience when it is added to my player. Assuming this is another catch bonus, what could this be? I am looking for a transparent screensaver. Or a way for there to be no screen saver, but instead of locking, it disables the mouse and most of the keyboard, until I hit an unlock key. Am I using beta or stable? I have been doing so many sudo apt-get update/(dist-)upgrade since yesterday and  something happend - so that I am confused now whether I am using still beta or the stable version.   How do I figure that out? Why modules with no variables? What is the best way(s) to fake function overloading in Javascript?   I know it is not possible to overload functions in Javascript as in other languages.  If I needed a function with two uses foo(x) and foo(x,y,z) which is the best / preferred way:   Using different names in the first place Using optional arguments like y = y || 'default' Using number of arguments Checking types of arguments Or how? How to turn cheats on or off Age limit is too strict I'm not entirely clear on how Counterspell works, when trying to counter higher-level spells: the CS description only talks about disrupting a creature you can see, within 60 feet, casting a spell.   However, when trying to counter a higher level spell:   Do I know what spell is being cast?  Do I at least know (somehow intuit, based on VSM components) the level of the spell? Or can I tell the spell/level of the spell by sensing a disturbance in The Weave? (I.e., if the spell is being cast using Subtle Spell, can I still tell what's going on?)   The point of the question is to determine how fruitful CS can be in combat--if I know what the other guy/gal is casting (or at least the level), I can decide whether I want to spend my L8 slot to counter his/her L8 slot. But if I have no idea, and I end up using a L8 slot to counter a L3 spell... seems a bit painful.  Hope this made sense! How to split by commas that are not within parentheses? Pure virtual destructor in C++ Forgive the possibly naive question, but I'm returning to a basic undergrad-level study of chaotic dynamical systems and can't quite seem to reconcile the notion that in order for a dynamical system to be considered chaotic, it must have positive global Lyapunov exponents. Such exponents, of course, drive the divergence of trajectories. However, topological transitivity implies that trajectories can get arbitrarily close as well over some finite time. It seems that positive Lyapunov exponents would disallow this mixing. Is there a point at which these positive exponents no longer describe the system, and the mixing behavior begins? so someone tells me i need to call a few people.  they send me a vCard called contacts.vcf.  i import it.  i open my phone app and start to dial, but wait...i don't know their names.  How do i look up a recent vCard on my phone?  How do i know who's contact i've been sent?  when i navigate to a .vcf file, i can't open it.  all i can do is import it.  polaris office won't import/open it.  is there an android txt editor i can use to peruse a vCard?  yours truly, Confused by vCards Note 3, kit kat write some AMPscript to skip a record if its empty I have a data extension with a CustomerId(PK) that has multiple Productid's as Productid1, ProductId2, ProductId3...ProductId10.   Some of the Productid's are empty for some Customers and I'm trying to write some AMPscript if the productIdx is empty to show the next one.  I'm trying to display 6 products in an email and at the moment when I preview the email, if from the first six Products one doesn't have a value(is empty) I get the error "The subscriber preview failed to generate. Review the details, correct all issues, and try again. Product1 not found"  I want to skip the product that is NULL and go to the next one available.  %%[ SET @customerId = [customerId]  SET @customer_rows = LookupRows("PRL","customerId",@customerId) IF Rowcount(@customer_rows) &gt; 0 THEN SET @customer_row = ROW(@customer_rows, 1)  SET @product_count = 0  SET @productId1 = FIELD(@customer_row, "productId1")  IF NOT EMPTY(@productId1) THEN SET @product_rows = LookupOrderedRows("PI_UK", 1,"Normal_SalePrice Desc", "ProductCode", @productId1)  IF RowCount(@product_rows) &gt; 0 THEN  SET @product_count = ADD(@product_count,1) ELSE  SET @product_count = ADD(@product_count,0) ENDIF ELSE SET @product_count = ADD(@product_count,0) ENDIF    SET @productId2 = FIELD(@customer_row, "productId2") IF NOT EMPTY(@productId2) THEN SET @product_rows = LookupOrderedRows("PI_UK", 1,"Normal_SalePrice Desc", "ProductCode", @productId2) IF RowCount(@product_rows) &gt; 0 THEN SET @product_count = ADD(@product_count,1) ELSE SET @product_count = ADD(@product_count,0) ENDIF ELSE SET @product_count = ADD(@product_count,0) ENDIF  SET @productId3 = FIELD(@customer_row, "productId3") IF NOT EMPTY(@productId3) THEN SET @product_rows = LookupOrderedRows("PI_UK", 1,"Normal_SalePrice Desc", "ProductCode", @productId3) IF RowCount(@product_rows) &gt; 0 THEN SET @product_count = ADD(@product_count,1) ELSE SET @product_count = ADD(@product_count,0) ENDIF ELSE SET @product_count = ADD(@product_count,0) ENDIF  and so on till ProducId10...   I have uploaded a photo with the PRL Data extension Minimum of $\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}$ What is the minimum of $$f(a,b,c):=\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}$$ where $a,b,c$ are positive real numbers?  When $a=b=c$, we have $f(a,b,c)=\dfrac{3}{\sqrt{2}}\approx 2.12$  When $a=1,b=c\rightarrow\infty$, we have $f(a,b,c)\rightarrow 2$. So the minimum is at most $2$. Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has My attempt  Note- Addition is under $mod$ $d$  Let $G = (a^0,a^1,a^2.....a^{n-1})$  $n=kd$  Let $H_d = (a^{0k},a^{1k},a^{2k}......a^{{(d-1)}k})$  For $a^{z_1k},a^{z_2k} \in H_d$  $a^{z_1k}a^{z_2k} = a^{{(z_1+z_2)}k} \in H_d$  $H_d$ is closed  For $a^{zk} \in H_d$  $a^{zk} (a^{zk})^{-1}=a^0$  $(a^{zk})^{-1} = (a^{-1})^{zk}$  Since $a^{-1}$ is $a^{n-1}$ we can rewrite it as   $(a^{zk})^{-1} = (a^{n-1})^{zk}=a^{z(n-1)k} \in H_d$  Since $(a^{zk})^{-1} \in H_d$ and $H_d$ is closed, $H_d$ is a subgroup.  I can easily prove the 3rd part by using Lagrange's theorem.  I have no idea how to prove that only $1$ subgroup of order $d$ exists. Maybe by proving that the elements of the $2$ groups have to be the same?  I would really appreciate if someone could verify my proof so far and give some hints to complete the proof. My laptop is filled with viruses and Windows XP is just becoming impossible to work with.   I've been interested in Ubuntu for a while, so, would I be able to use something like Debian to clear my HDD and OS and then install Ubuntu and start fresh? Can I store my pixels somewhere so I don't lose them when I die? I die all the time. My pixel balance hovers around zero as a result. I'm trying to save up for armor but my nonstop deaths are making that difficult.  Is there anywhere I can store my pixels so that when I die, I won't lose a bunch of them?