An Artificer Armorer acquires the class feature &quot;Arcane Armor&quot; at level 3. With that, the armor provides a special simple weapon (Thunder Gauntlets or Lightning Launcher). Now all of this &quot;Arcane Armor&quot; is one entity (from the perspective of infusions). This changes when you are level 9, then you acquire the &quot;Armor Modifications&quot; class feature, which lets you count your Arcane Armor as four different entities (again from the perspective of infusions). Can you apply a weapon infusion (Enhanced Weapon) to the special simple weapon (Lightning Launcher) before you get &quot;Armor Modifications&quot; as early as level 3 if no other infusions currently affect the Arcane Armor (no Enhanced Defense, etc.)? I have  regarding whether or not you can infuse the weapon when you hit level 9 with &quot;Armor Modifications&quot;.  I am asking explicitly can you do this without the &quot;Armor Modifications&quot; class feature.
At 9th level, the Armorer Artificer (from Tasha's Cauldron of Everything) gains the &quot;Armor Modifications&quot; feature :  You learn how to use your artificer infusions to specially modify your Arcane Armor. That armor now counts as separate items for the purposes of your Infuse Items feature: armor (the chest piece), boots, helmet, and the armor’s special weapon. Each of those items can bear one of your infusions, and the infusions transfer over if you change your armor’s model with the Armor Model feature. In addition, the maximum number of items you can infuse at once increases by 2, but those extra items must be part of your Arcane Armor.  This special weapon is called 'Thunder Gauntlets' (a simple melee weapon) for the 'Guardian' Armor Model, and 'Lightning Launcher' (a simple ranged weapon) for the 'Infiltrator' Model. But I am wondering which Artificer Infusions are appropriate for this special weapon ? Is it only the 'Enhanced Weapon' and 'Radiant Weapon' infusions, or are there others ?
Let $A_n$ denote an $n \times n$ tridiagonal matrix.  $$A_n=\begin{pmatrix}2 &amp; -1 &amp; &amp; &amp; 0 \\ -1 &amp; 2 &amp; -1 &amp; &amp; \\ &amp; \ddots &amp; \ddots &amp; \ddots &amp; \\ &amp; &amp; -1 &amp; 2 &amp; -1 \\ 0 &amp; &amp; &amp; -1 &amp; 2 \end{pmatrix} \quad\text{for }n \ge 2$$  Set $D_n = \det(A_n)$  Prove that $D_n = 2D_{n-1} - D_{n-2}$ for $n \ge 4$. Is $\{0\}$ a field? Consider the set $F$ consisting of the single element $I$.  Define addition and multiplication such that $I+I=I$ and $I \times I=I$ .  This ring satisfies the field axioms:   Closure under addition.  If $x, y \in F$, then $x = y = I$, so $x + y = I + I = I \in F$. Closure under multiplication.  $x \times y = I \times I = I \in F$ Existence of additive identity.  $\forall x \in F$ (i.e., for $x=I$), $x + I = x$, so $I$ is the additive identity. Existence of mulitiplicative identity. $\forall x \in F, x \times I = x$, so $I$ is the multiplicative identity. Additive inverse. $\forall x \in F, \exists y = I \in F: x + y = I$ Multiplicative inverse. $\forall x \in F, \exists y = I \in F: x \times y = I$.  However, because the additive identity need not have a multiplicative inverse, this is a vacuous truth. Commutativity of addition.  $\forall x, y \in F, x + y = I = y + x$ Commutativity of multiplication.  $\forall x, y \in F, x \times y = I = y \times x$ Associativity of addition.  $\forall x, y, z \in F$, $(x + y) + z = I + I = I$ and $x + (y + z) = I + I = I$, so $(x + y) + z = x + (y + z)$ Associativity of multiplication.  $\forall x, y, z \in F$, $(x \times y) \times z = I \times I = I$ and $x \times (y \times z) = I \times I = I$, so $(x \times y) \times z = x \times (y \times z)$ Distributivity of multiplication over addition. $I \times (I + I) = I$ and $I \times I + I \times I = I$, so $\forall x,y,z \in F, x(y+z) = xy+xz$   Based on the above, $\{I\}$ seems to qualify as a field.  If $I$ is assumed to be a real number, then the unique solution of $I + I = I$ and $I \times I = I$ is, of course, $I = 0$.  So, is {0} a field, or is there generally considered to be an additional field axiom which would exclude it?  Specifically, is it required for the multiplicative identity to be distinct from the additive identity? How to prove one has spent time in the non-Schengen European microstates, in order to pause the Schengen clock? I am considering staying in Monaco, San Marino, or Vatican City before I can enter the Schengen area again. , it is valid to stay in these three micro-states in order to stop the Schengen clock. However, also according to the answer:  Problems will arise when the visitor ultimately leaves the zone and must undergo a Schengen exit inspection. At this point the person may be asked to prove that they are not an overstayer and the border guard will be entitled to see hard evidence in the form of official documentation. There was a case where an individual attempted to show that his mobile phone registered to a tower outside of the zone and this failed obviously: radio waves have no respect for nation borders but also one could mail the SIM card to a friend in a far away land, put in a phone where it registers to the tower and then mail it back. Apparently hotel receipts can be too easily forged to be successful as evidence. What the border guard will want to see is a passport stamp from the local constabulary. But the constabulary is under no obligation to issue one, so success is down to personal impact and articulation skills.  I'm not sure if I could get a stamp from the local constabulary. However, I always use AirBnB to stay, and the reservation email and the mobile app might be far more reliable than a random hotel reservation document. So, does the AirBnB reservation email work as a proof of staying there? Or is there any better document as a proof of staying (&quot;better&quot;, in terms of ensuring that I don't pay the overstaying penalty)? I will likely leave the Schengen area ultimately from Frankfurt International Airport. Following on from this question:   It seems all feats carry over to your new form if your new form is capable of using them (so Mounted Combatant and Inspiring leader would usually be ruled as unusable in most circumstances). But what about Tough?     Your hit point maximum increases by an amount equal to twice your   level when you gain this feat. Whenever you gain a level thereafter,   your hit point maximum increases by an additional 2 hit points.   Would this increase your maximum HP by the same amount when in the form of a rat, or brown bear? What's the single-word for "left or right handed"? 'Male'/'female' is to 'gender' as 'left-handed'/'right-handed 'is to...?  Is there a word to describe this? For example, if I ask a guy     What's your ____?   It should mean I'm asking whether he's left or right-handed.  Another example could be     Our designs are not biased  against your ____.   Basically, I'm looking for something that means the state of being left- or right-handed which could be used analogously as gender.  EDIT: Sorry for the delay in the edit, but I was tied up. There are some points I'd like to clarify:   I'm not looking for a way to paraphrase my questions. I'm looking for a single word. I know people normally ask something along the lines of "Are you left-handed or not?" People also ask "Are you afraid of the dark?" instead of "Are you scotophobiac?". The word for it,  still exists, right? It has been pointed out that I should go with Our designs are not biased against left-handed people as that is what I mean. But that is not necessarily what I mean.    For example, let's say there is a washbasin with the tap on the right. Clearly, it's biased against lefties. Sometimes, you come across a washbasin with a tap on the left. (The logic being: you use your left hand to turn the tap as your right one's dirty). But, your right hand might not always be dirty, in which case, it's biased against righties.  A washbasin with the tap on the center is, then, handedness-blind or chirality-blind, if you will. (I foresee that some would dwell on Our designs are symmetrical. Please don't.)  I'm looking for a term that would be applicable here, as well as in the 1st example.  My favorite so far is chirality, suggested by Dan Bron in a comment (with 25 upvotes!) But, I'm reluctant to use it because there's no hard proof it's used in that sense  If we are talking about male-female, gender works perfectly. What's your gender? and Our designs aren't biased against your gender. , both work perfectly here.  Sorry for the late edit again. If the consensus is that I rollback, I will. Let me know in the comments. I want to redirect all requests from example.com to www.example.com.   Preferably, this should happen at DNS level. I tried using PTR records, but that simply fails, returning a 404.  wwww.example.com is an ALIAS for an Elastic Load Balancer.  What’s the simplest way to achieve this? How do I extract all the external links of a web page and save them to a file? How do I extract all the external links of a web page and save them to a file?  If you have any command line tools that would be great. I recently setup a new computer for my parents with windows 10 home. I made two local accounts for them - no microsoft accounts. I also would like to keep them without a password. Problem is now that windows automatically signs in with the last used account. No lock/login screen.  I tried a number of answers from similar questions here but none worked. Since it's a home version there are no group policies and the method using task scheduler does not work because accounts with no password are not allowed to create such tasks.  Are there other options to force windows to show a user list on startup without setting passwords for the accounts? Why does a monopole not radiate energy in electodynamics? How exactly does Knuth's Up-Arrow notation work? I've done some research, and found this on Wikipedia. \begin{matrix}a\uparrow b=a^{b}=&amp;\underbrace {a\times a\times \dots \times a} \\&amp;b{\mbox{ copies of }}a\end{matrix} \begin{matrix}a\uparrow \uparrow b&amp;={\ ^{b}a}=&amp;\underbrace {a^{a^{{}^{.\,^{.\,^{.\,^{a}}}}}}} &amp;=&amp;\underbrace {a\uparrow (a\uparrow (\dots \uparrow a))} \\&amp;&amp;b{\mbox{ copies of }}a&amp;&amp;b{\mbox{ copies of }}a\end{matrix} I'm still a bit confused on this topic. I've done a lot of research, but I can't seem to understand this. Could somebody explain this in an understandable way? From what I can gather, for example 2↑↑3 would be 2^2^2 = 16? Then 2↑↑↑3 would be 2^2^2^2 = 256? Am I correct, or have I mis-interpreted this? How to prove that any idempotent matrix is diagonalizable? $X$ and $Y$ are independent $U(0,1)$ random variables.   I have to find $E[X|X&gt;Y]$.   I found it out by integrating $\int_0^1 \int_y^1 x dxdy$ to get $\frac{1}{3}$ as the answer but this is wrong according to the answer key. What is the mistake that I have made? NS list does not match list from parent zone I'm attempting to figure out an error message that I got from dnsstuff.com when examining my DNS records.  The error reads as follows.     NS list does not match list from parent zone. This should be addressed because queries for this domain may require an extra lookup (and more overhead) because there is no direct relationship between the NS records at the parent and the NS records at the authoritative servers. This can cause delays. The mismatched NS list is:      nameserver ns1.domain.co. | xxx.xx.xxx.xxx is missing NS2.domain.co. | yy.yyy.yy.yyy   There are a couple questions I have regarding this.   What is the difference between a parent and authoritative zone?  In other forum posts I've seen, the seem to be used interchangeably (although that could be my misperception). What does it mean for the NS list not to match the list from the parent zone?  What is "the list from the parent zone" to which they refer? How might you recommend that I resolve this?   In case this affects any answers, I'm running Virtualmin on Ubuntu 12.04.  Any help is appreciated.  Many thanks in advance! I can't update 12.04 LTS. The Update Manager shows this:  CD/DVD 'Ubuntu 12.04 LTS _Precise Pangolin_ - Release i386 (20120423)' is required Please insert the above CD/DVD into the drive '/media/cdrom/' to install software packages from it.   The image I downloaded and burned to CD is from  the PC (Intel x86) desktop CD version. I burned many CDs but the result is the same. Count down in timeout is cut off The time out countdown which is flying in is missing half of the number.  Note the 33 here:        Can this be fixed please? General solution to the PDE $xU_x+yU_y=0$ Solve the equation $xU_x+yU_y=0$.   From Partial Differential Equations: An Introduction, 2nd Ed. (Strauss, pg. 10). There are no boundary conditions.  Solution: The PDE can be written $(x,y)\cdot\nabla U(x,y)=0$, implying that the vector $(x,y)$ is tangent to the PDE's characteristic equation. Then I can write $dy/dx=y/x$, and to solve this ODE,  $$\frac{dy}{dx}=\frac yx \\ \ln y=\ln x+c_1 \\ y=cx \\ y/x=c$$  Hence, the PDE is dependent on $c$ and I can write $U(x,y)=f(y/x)$ for some function $f$, solving the problem.  Question: Is this solution correct? The hint for the question (supplied by the professor) said I should use a substitution of variables, but this seems reasonably valid. Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$. Suppose $f$ is Riemann integrable on $[0,1]$ and continuous at 0. Show that $$\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0).$$   Can anyone share some insight on this one? I have no idea where to begin. Maybe a substitution? Can I use a 23 W CFL in a fixture that's rated for a 60 W incandescent? I have a lamp that is rated at 60 Watts for an incandescent bulb with a disclaimer to use a 13 Watt bulb instead when using a CFL replacement. Do I really need to respect that disclaimer? Would not a 23 Watt CFL be just as safe to use? It still draws less power than a 60 Watt incandescent, right? Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets? The  asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of mathematics ranging from exercises in freshman classes to constructing useful counterexamples for some advanced questions. Solutions of this equation are often called . Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online?