related to  I think. I'm trying to understand the distinction between &quot;shall&quot; and &quot;&quot;shalt&quot; but only in a specific case: In the final line of John Donne's Holy Sonnet, &quot;Death be not proud&quot; he writes,  And death shall be no more; Death, thou shalt die.  He uses both forms. I can guess at all sorts of possibilities, including biblical allusion, but all I have is guesses. Is there any difference in meaning between the two on a grammatical level, or should I be posting this on a literature board for poetic interpretation?
In Shakespeare's Macbeth, the Third Witch says to Banquo: "Thou shalt get kings, though thou be none" (1.3.65); if I want to quote that line and write it in the third person singular, how should I conjugate the verbs "shall" and "be" correctly?
How can a point-particle have properties? I have trouble imagining how two point-particles can have different properties.  And how can finite mass, and finite information (ie spin, electric charge etc.) be stored in 0 volume?  Not only that, but it can also detect all fields without having any structure. Maybe it can check curvature of spacetime to account for gravity, but how can a point contain the information of what the other fields-vectors are? This seems to mean that also the information/volume in space is infinite.  Mathematically, a point cant have any intrinsic structure, so how does physics which is a mathematical theory explain this? To my knowledge there are three types of acceleration when a body (e.g. a rod) is moving in a circle about an axis. These are:   Angular acceleration : this is the rate of change of angular velocity. Tangential acceleration : this is the linear acceleration of the system in a tangential direction to the circle and equals the radius times the angular acceleration. Radial/centripetal acceleration : this is the linear acceleration of the system that is directed inwards towards the center of the circle.   I also think there are two types of velocity:   Linear velocity: this is its velocity in the tangential direction and is constantly changing Angular velocity or angular frequency: this is the rate of change of angle.   Is the above correct? And have I missed anything? Is  free for business platforms?  Has Ubuntu changed its conditions about using the OS for profit purposes? velocity of an object after leaving a ramp modulo version of the quadratic formula and Euler's criterion Use the modulo version of the quadratic formula and Euler's criterion to decide if the following has a solution or not.  $2x^2+5x+8 \equiv 0\pmod{37}$  I'm not sure how I would use what was being asked of me to decide if this has a solution or not, but I have came to the conclusion that it does not, because I plugged in every possible answer $0-36$, and none of them were congruent to zero.  The way people have answered the question, isn't exactly the way I need.  I have made some progress, but I'm not exactly sure how to finish:  $2x^2+5x+8 \equiv 0\pmod{37}$  $x^2+21x+4\equiv0\pmod{37}$  $x^2+58x+841\equiv837\pmod{37}$  $(x+29)^2\equiv23\pmod{37}$  I know that if $p$ is an odd prime and $p$ doesn't divide $a$, then $x^2\equiv a\pmod{p}$ has a solution or no solution depending on whether $a^\frac{p-1}{2}\equiv 1  \space\space \text{or}\space -1\pmod{p}$.  This is where I get stuck.  Can someone help me from here?  I have a feeling this problem has no solutions, so could someone also explain to me what to do if a problem like this did have solutions. What is the equation for the tension on the ends of a cable suspended at different heights? I'm looking for an equation to find the tension on the ends of a cable suspended between two poles (one higher than the other) with no load but the cable itself.    I determined that the tension would be different on each end, that the shape of the suspended cable would be a  truncated at one end, and that the following would be the variables necessary in the equation:   cable weight cable length vertical distance between ends horizontal distance between ends   Some links that could be helpful: What does the 'B' (or bonus) mean on a basketball scoreboard? onConfigurationChanged not getting called Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$ I want to evaluate the following integral via complex analysis $$\int\limits_{x=0}^{x=\infty}e^{-ax}\cos (bx)\operatorname d\!x \ \ ,\ \ a &gt;0$$  Which function/ contour should I consider ? Android OS without Google Services? I have a Sony Xperia Z with version 4.1.2 running.  My question is about removing all of the Google baggage from the phone.  I have no Google account tied to my phone and would really like to get rid of all traces of Google from my phone for a few reasons:   Battery performance: Google services ranks in the top 3 of what uses up my battery Privacy: I try to minimize what Google siphons from my phone with the exception of Google maps Less Dependency: I don't want to be dependent on one company for all my needs.   So are there any Android versions out there that are minimalistic and do not invade your privacy? Let $a,b,c\in \mathbb{Z}$. If $ac&gt;bc$ and $c&gt;0$, then $a&gt;b$   I think I would use contrapositive to prove this. But I am not sure proper contrapositive statement.   Is it If $a&lt;b$, then $ac&lt;bc$, and $c&lt;0$.? If so, contrapositive is not a good choice, isn't it? Image data URI and SEO Do you think the use of image data URI is SEO friendly?   On the one hand saves you a HTTP request. On the other hand it really messes up your code. Especially for image files larger than 20KB or moving GIF image files of up to 200KB, the quantity of code inserted is enormous. As Googlebot reads usually from top to bottom, all data after the image data URI encoding will be harder to rank well in Google.   Consider that image data URI is not in the CSS files as they should normally be and for the time being I can use only TinyMCE editor which provides me with just two options, either insert image with the image data URI method or the traditional image link.   I would like to know which is more search engine friendly. How does the Deposit-User work? Infinite distinct factorizations into irreducibles for an element Consider the factorization into irreducibles of $6$ in $\mathbb{Z}[\sqrt{-5}]$. We have $6=2 \times 3$ and  $6=(1+\sqrt{-5}) \times (1-\sqrt{-5})$, i.e. $2$ distinct factorizations. And,  $$6^2=3 \times 3\times2\times2$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5}) \times (1+\sqrt{-5}) \times (1-\sqrt{-5})$$ $$=(1+\sqrt{-5}) \times (1-\sqrt{-5})\times3\times2.$$ More generally, $6^n$ will have $n+1$ distinct factorizations into irreducibles in $\mathbb{Z}[\sqrt{-5}]$ by a simple combinatorial argument. But, can we construct a ring in which there exists an element that has an infinite number of distinct factorizations into irreducibles? To make life harder, can we construct an extension of $\mathbb{Z}$ in which this happens? I have been thinking about this for a while and have managed to find no foothold.. Any help is appreciated. Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ Ignoring invalid input features with Intersection tool in QGIS? In QGIS 2.18, when I used the Vector > Geoprocessing Tools > Intersection tool, I was able to check an option which said "Ignore NULL geometries [optional]".  Now I've downloaded QGIS 3.2 and that option no longer exists. But when I try to create the intersection between two layers I'm working on, I get a message saying that there is an invalid geometry somewhere and that I should either fix it it or "change the Processing setting to the 'Ignore invalid input features' option."   But that option doesn't exist! Or if it does exist, I just can't find it anywhere.  Does anyone know how/where to change this setting in QGIS 3.2? Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients} Let $W = \{ p(B) : p \text{ is a polynomial with real coefficients}\}$, where $$B= \begin{pmatrix} 0 &amp; 1 &amp; 0\\  0 &amp; 0 &amp; 1\\  1 &amp; 0 &amp; 0 \end{pmatrix}$$  Which of the following possibilities presents the tightest bounds on the dimension $d$ of the vector space $W$?     $4 ≤ d ≤ 6$    $6 ≤ d ≤ 9$    $3 ≤ d ≤ 8$    $3 ≤ d ≤ 4$ How far can one get in analysis without leaving $\mathbb{Q}$? Suppose you're trying to teach analysis to a stubborn algebraist who refuses to acknowledge the existence of any characteristic $0$ field other than $\mathbb{Q}$.  How ugly are things going to get for him?  The algebraist argues that the real numbers are a silly construction because any real number can be approximated to arbitrarily high precision by the rational numbers - i.e., given any real number $r$ and any $\epsilon&gt;0$, the set $\left\{x\in\mathbb{Q}:\left|x-r\right|&lt;\epsilon\right\}$ is nonempty, thus sating the mad gods of algebra.  As @J.M. and @75064 pointed out to me in chat, we do start having some topology problems, for example that $f(x)=x^2$ and $g(x)=2$ are nonintersecting functions in $\mathbb{Q}$.  They do, however, come arbitrarily close to intersecting, i.e. given any $\epsilon&gt;0$ there exist rational solutions to $\left|2-x^2\right|&lt;\epsilon$.  The algebraist doesn't find this totally unsatisfying.     Where is this guy really going to start running into trouble?  Are there definitions in analysis which simply can't be reasonably formulated without leaving the rational numbers?  Which concepts would be particularly difficult to understand without the rest of the reals? Integral $ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $ I need to compute the improper integral $$ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $$ using contour integration and possibly principal values.  Trying to approach this as I would normally approach evaluating an improper integral using contour integration doesn't work here, and doesn't really give me any clues as to how I should do it. This normal approach is namely evaluating the contour integral $$ \oint_{C}{\frac{z^2}{\cosh\left(z\right)}\mathrm{d}z} $$ using a semicircle in the upper-half plane centered at the origin, but the semicircular part of this contour integral does not vanish since $\cosh\left(z\right)$ has period $2\pi\mathrm{i}$ and there are infinitely-many poles of the integrand along the imaginary axis given by $-\pi\mathrm{i}/2 + 2n\pi\mathrm{i}$ and $\pi\mathrm{i}/2 + 2n\pi\mathrm{i}$ for $n \in \mathbb{Z}$. The residues of the integrand at these simple poles are $-\frac{1}{4}\mathrm{i}\pi^{2}\left(1 - 4n\right)^{2}$ and $\frac{1}{4}\mathrm{i}\left(4\pi n + \pi\right)^{2}$, so that even when we add up all of the poles, we have the sum $4\pi^{2}\mathrm{i}\sum_{n = 0}^{\infty}\,n$, which clearly diverges.  Any hints would be greatly appreciated. 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps I am looking for some examples of closed, orientable 3-manifolds $M$ and $N$ and a homomorphism $\phi : \pi_1(M) \to \pi_1(N)$ such that $\phi$ is not induced by any continuous map $f : M \to N$.  Are there examples of this occurring for lens spaces?  I do not believe that this phenomenon can occur for maps between surfaces.