Why is &quot;having&quot; written? And not &quot;to have&quot;  I was so close to having a perfect activity week on my Apple Watch.
What is the difference between these two:     Suzuki was nearly close to go out of business just after the World War period.   Vs.     Suzuki was nearly close to going out of business just after the World War period.(from a video)   When talking about the past, do these two sentences different from each other? Like, if you use verbing(going) with infinitive(to) in the past, does it mean that there is another event happening? Or none.
Let $A$ be a nonempty and bounded below, and define $B= \{b\in \mathbb{R}: b$ is a lower bound for $A\}$. Show sup$B$ = inf$A$.   So far I have: Let $A$ be nonempty and bounded below. This implies $\exists l \in A, \forall a \in A, l\leq a$ and $l =$ inf$A$. Let $B = \{b\in \mathbb{R}: b$ is a lower bound for $A\}$ and let $M=$ sup$B$. This implies $\exists b\in B, \forall b \in B, b\leq M$. By definition of $B$, we know inf$A \in B$. Since $b\leq$ sup$B$, with sup$B$ the largest element in $B$, we have inf$A \leq M =$ sup$B$, so inf$A \leq$ sup$B$.  I realize I have to prove that sup$B \leq$ inf$A$ to get that sup$B$=inf$A$. I am having trouble doing so.   Part B: Use (a) to explain why there is no need to assert that greatest lower bounds exist as part of the Axiom of Completeness. Origin/reason for the expression "on the bus" instead of "in the bus" Old fantasy book with a party finding coloured stones having powers over fire, water, mood I'm trying to remember the name of a book series of which I remember only the following, with Google yielding no results.   the name of the author starts with a Z   the main character is a knight in an household with a name sounding like Malachai who goes on a quest with six others guys and girls (a bard, another knight, a priest, etc.) and each of them finds a stone of colour which has a power on various things (like fire, their mood or water) and then they set toward a quest to beat some ancient evil. I used to find the book at the local library 10 years ago in France (but it was translated). How to get the date in a batch file in a predictable format? In a batch file I need to extract a month, day, year from the date command.  So I used the following, which essentially parses the Date command to extract its sub strings into a variable:  set Day=%Date:~3,2% set Mth=%Date:~0,2% set Yr=%Date:~6,4%   This is all great, but if I deploy this batch file to a machine with a different regional/country settings, it fails because month, day and year are in different locations.   How can I extract month, day and year regardless of the date format? Hi I want to try Ubuntu 20.04 without installing it due to some driver issues in my laptop. But I already have 2 OS ( Windows 10 and Ubuntu 20.04 [Dualboot] ), so will trying Ubuntu mess with the already installed Operating systems? And I know how to make live usb and booting from it but don't know how to exit it and then bring my laptop back to normal. Tried finding procedure on internet but reliable results are not found. I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here? Display of content-type I've got custom content-type with several groups and fields.   I want to change default display of that content-type. In which file can I find appropriate code? Who made the decision for Gandalf's promotion from 'grey' to 'white'? In the first book of the LoTR, after his fight with the Balrog of Moria, Gandalf the Grey changed to .   My question is, who made the decision to 'promote' him from grey to white? Was it ? Or was it the ? Or was it the ? Number of equivalence relations on a set If a set has $n$ elements then what are maximum number of equivalence classes and equivalence relations possible on it? Can you link external USB hard drives in a RAID-style system? Is my solution correct for solving $\cos(z)=2$, $z\in \mathbb{C}$ Rectangles around cells in table How to add a Skype indicator? Suppose that an entire function $f(z)$ satisfies $\left|f(z)\right|\leq k\left|z\right|^n$ for sufficiently large $\left|z\right|$, where $n\in\mathbb{Z^+}$ and $k&gt;0$ is constant. Show that $f$ is a polynomial of degree at most $n$. Question regarding an inequality How to prove that $$ \frac{x_1}{1+x_1^2}+\frac{x_2}{1+x_1^2+x_2^2}+\cdots+\frac{x_n}{1+x_1^2+\cdots+x_n^2}&lt;\sqrt{n} $$ knowing that $(x_n)$ is a positive sequence ? I looked up all kinds of inequalities such AM-GM, Chebyshev, Cauchy-Schwarz, but I couldn't manage to obtain anything useful.. Can anyone help ? A gold reviewer badge? Why Didn't People Think That Voldemort Died After His Attack on Baby Harry? After the Avada Kedavra curse rebounded from Harry onto Voldemort, Voldemort disappeared. I'm curious as to why so many key players believed Voldemort was still "alive" somewhere, his powers decimated, but, under the right circumstances, able to return to full power. It seems the witches and wizards in chapter one of Philosopher's Stone, The Boy Who Lived, were happy to believe that Voldemort was gone forever. Why didn't everyone believe Voldemort had died, rather than just disappeared? Was it the lack of a body? Or were there other reasons?  Here's a couple of quotes from Philosopher's Stone if anyone wants to review them. Otherwise, just disregard.     ‘A fine thing it would be if, on the very day You- Know-Who seems to have disappeared at last, the Muggles found out about us all. I suppose he really has gone, Dumbledore?’   ‘It certainly seems so,’ said Dumbledore. ‘We have much to be thankful for.’   Philosopher's Stone - page 13 - Bloomsbury - chapter 1, The Boy Who Lived   ‘But what happened to Vol– sorry – I mean, You-Know-Who?’   ‘Good question, Harry. Disappeared. Vanished. Same night he tried ter kill you. Makes yeh even more famous. That’s the biggest myst’ry, see ... he was gettin’ more an’ more powerful – why’d he go?   ‘Some say he died. Codswallop, in my opinion. Dunno if he had enough human left in him to die. Some say he’s still out there, bidin’ his time, like, but I don’ believe it. People who was on his side came back ter ours. Some of ’em came outta kinda trances. Don’ reckon they could’ve done if he was comin’ back.   ‘Most of us reckon he’s still out there somewhere but lost his powers. Too weak to carry on. ’Cause somethin’ about you finished him, Harry. There was somethin’ goin’ on that night he   hadn’t counted on – I dunno what it was, no one does – but somethin’ about you stumped him, all right.’   Philosopher's Stone - pages 46-47 - Bloomsbury - chapter 4, The Keeper of the Keys Cycles Emit Light from area on Texture So I have a giant object that is completely uv unwrapped. I would like to make areas of the object with a specific area of texture emit light.   The problem is that this object (and it is only one object) only has one material. I would like the lava to emit light, but I cannot move it to a separate material without breaking something.  I'd like to find a method where I can select a part of the texture and tell blender that whatever has that part of the texture emits light.  Is this possible?  Thanks. Why is propagation of uncertainties quadratic rather than linear? 1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation:  if $C = A+B$  or  $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = \frac{A}{B}$ $$\frac{\Delta C}{C} = \frac{\Delta A}{A}  + \frac{\Delta B}{B}$$ if $C = A^m$ $$\frac{\Delta C}{C} = |m|\frac{\Delta A}{A}$$   These formulas are derived from the expression for the differential of a function of multiple variables:  if $C = f(A,B)$ $$ dC = \frac{\partial C}{\partial A}dA + \frac{\partial C}{\partial B}dB \Rightarrow \Delta C = \frac{\partial C}{\partial A}\Delta A + \frac{\partial C}{\partial B}\Delta B$$  and I think that makes sense because the value C is just a function of two variables that happen to be measurements.  2) But this morning, I was told that this is wrong and I should actually use these instead:  if $C = A+B$  or  $C = A-B$ $$(\Delta C)^2 = (\Delta A)^2 + (\Delta B)^2$$ if $C = AB$ or $C = \frac{A}{B}$ $$\left(\frac{\Delta C}{C}\right)^2 = \left(\frac{\Delta A}{A}\right)^2  + \left(\frac{\Delta B}{B}\right)^2$$  which are apparently derived from a general formula:  $$(\Delta C)^2  = \left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...$$  or   $$\Delta C  = \sqrt{\left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...}$$  3) So:   Why is this formula better?  Where does it come from? What does it actually represent? (Do I recognize the shape of a norm in that last formula?)  What is wrong with the formula of the differential?   I'm asking a lot, but the propagation of uncertainty always confused the ship out of me. Do Skyrim mods work with the Special Edition? I typically play Skyrim with a number of mods installed, and while I'm excited to try the Special Edition, there are a few mods that I'd much rather not play without.  Can I install mods built for the normal Skyrim game with the Special Edition, or do I have to wait until mod authors write new versions before I can play with those mods?