I'm sure we'd all rather I became a bit more self-sufficient.   Using became feels right, but I would appreciate anyone who could explain what's going on grammatically here. I think become is in the subjunctive, so maybe most correctly I should say     I'm sure we'd all rather that I become a bit more self-sufficient.   Is that strictly necessary? And regarding my original construction: am I wrong to feel so right?
What is the difference between:   The company would rather each employee be provided with ID card.  The company would rather each employee were provided with ID card.
FoxTrot Bill Amend Problems So I found this on the Wolfram website today:     So I was wondering about how one might be able to (if possible) solve those four problems by hand. Here are the problems, $\LaTeX$ed:    $ \lim_{x \to +\infty} \dfrac {\sqrt{x^3-x^2+3x}}{\sqrt{x^3}-\sqrt{x^2}+\sqrt{3x}} $ $ \displaystyle\sum_{k=1}^{\infty} \dfrac {(-1)^{k+1} k^2}{k^3+1} $  $ \dfrac {\mathrm{d}}{\mathrm{d}u} \left[ \dfrac {u^{n+1}}{(n+1)^2} \cdot \left[ (n+1) \ln u - 1 \right] \right] $  $ \displaystyle\int_0^{2\pi}\displaystyle\int_0^{\frac{\pi}{4}}\displaystyle\int_0^4 \left( \rho \cos \phi \right) \rho^2 \sin \phi \, \mathrm{d}\rho \mathrm{d}\phi \mathrm{d}\theta$     Ideas   The degree of the numerator is $\frac{3}{2}$. The degree of the denominator is $\frac{3}{2}$. The expression is of an indeterminate form, namely $\frac{\infty}{\infty}$, so we use l'Hoptial's Rule.  No ideas, really.  Derivatives are always pretty easy, although this one is a bit bashy. Basically bash Product and Chain Rules, etc.  Integration by Parts bash? The $\mathrm{d}\theta$ part is very trivial. I mean for the $\rho$ and $\phi$. I have removed Windows 7 using GParted, and want my computer to boot straight into Ubuntu, but I still get the dual boot screen, how can I fix this? First of all, I swear this is not homework, it's a question I was asked in an interview. I think I made a mess of it (though I did realise the solution requires recursion). Here is the question:  Implement the count() method which returns the number of nodes in a tree. If a node doesn't have either a left or right child, the relevant getXXChild() method will return null  class Tree {    Tree getRightChild() {     // Assume this is already implemented   }    Tree getLeftChild() {     // Assume this is already implemented   }    int count() {     // Implement me   } }   My reason for asking the question is simply curious to see the correct solution, and thereby measure how bad mine was.  Cheers, Tony Representative point of a cluster with L1 distance The representative point of a cluster or cluster center for the k-means algorithm is the component-wise mean of the points in its cluster. The mean is chosen because it helps to minimize the within cluster variances (which is to say that it is minimizing within cluster squared Euclidean distance, since its the same). Now, when I want to use a different distance metric, like L1 (Manhattan distance), I would be minimizing the within cluster absolute deviations (if I choose to). I was looking at what the centers calculation would be like, because the mean won't reduce the new objective function, and I found this on the Matlab documentation of their kmeans function for the distance parameter     cityblock - Sum of absolute differences, i.e., the L1 distance. Each centroid is the component-wise median of the points in that cluster.   Now, how did they come up with the component-wise median? How does a median minimize absolute deviations? Norm is sup of inner products (proof). Let $V$ be a vector space with an inner product $\langle.,. \rangle$ and associated norm $|| . ||$ Then:    Could I have a proof of this fact? Energy conservation of Virtual Particles - Quantum Fluctuation? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? How do I know if I'm working on a Virtual Machine or not? Is there a way to know if the Windows machine I'm working on is virtual or physical? (I'm connecting with RDP to the machine. If it's a virtual machine it is working and handled by VMWare). Same script opened in three different ways produces three different results. Why? I have a sample script (credit goes to ):  #!/bin/bash cat &lt;(cat /etc/lsb-release)   I save this script as somename.sh in my home directory.  Now, I try to open this file in three different ways:  sh somename.sh  bash somename.sh  ./somename.sh   So, I have two questions:   Why are the outputs for the above commands different though they are running the same script?   sh produces a Syntax error bash outputs the desired result ./ gives a Permission Denied error  Why is it necessary to give the script executable permission only when running the script using ./ and not necessary in the other cases?   Thanks in advance!  EDIT: The first part might be similar to the  linked one but, I did have a second question too. Acces VBA code combination not working, issue with exit sub? I'm very new at VBA and I can't seem to solve this problem. It seems like it should be an easy problem to fix, I just don't know how.   So what the code does: In the main form is a record. This record will be copied to another table bij pressing a button on the form. Before the copying begins, the code checks first if the 'OMnummer' has been filled in in the subform.  If not, a message box appears saying that the user should fill in the subform and the code stops running.   Secondly the code checks if the record is allready present in the other table. If so, a messagebox appears and the record will not be copied. If not, the record will be copied to the other table.   Both pieces of code work ok seperately. However, when I try to include both pieces in the same private sub, only the first one works. It may be something with the 'Exit Sub' code or I am not using the If - Then right.   Hope you can help me!  Monika   Private Sub KnopProjectVersturen_Click() On Error GoTo ErrProc  If IsNull(Me!Subform_OMnummers.Form!Omnr) Then  If MsgBox("Vul het OMnummer in. Je kan het project niet exporteren zonder OMnummer.")     Then       Exit Sub      DoCmd.OpenQuery "Qry_Depo_ControleAanwezig"  If DCount("Deponering.projectnummer", "Qry_Depo_ControleAanwezig") = 0 Then         DoCmd.SetWarnings False         DoCmd.OpenQuery "Qry_projectnaarDepot"          DoCmd.OpenQuery "Qry_ToevoegProjectDepot"         DoCmd.OpenForm "Depot_uitvoer", , , "[Projectnummer] = '" &amp; Me![Projectnummer] &amp; "' And [subID]=[subID]"     Me.Status = 8     DoCmd.Close acQuery, ("Qry_Depo_ControleAanwezig")     DoCmd.SetWarnings True  Else         MsgBox "Dit project bestaat al in de Depot_Uitvoer, verander de status in het projectformulier", vbInformation, "Example"         DoCmd.Close acQuery, ("Qry_Depo_ControleAanwezig")     End If  End If  End If    'Als er fouten zijn laat deze code een messagebox zien met het nummer en de melding.  ExitProc:  Exit Sub  ErrProc:     Select Case Err.Number     Case Else         MsgBox Err.Number &amp; "--" &amp; Err.Description         Resume ExitProc         End Select End Sub Making voltmeter accepting bipolar input voltage, using a microcontroller I want to build a very simple voltmeter using ATMEGA328 ADC. I can successfully measure up to 20v (using a voltage divider), but the problem is, I don't understand how to measure the voltage properly, if negative and positive terminals are switched.   Only way I could think of is adding another ADC input which is responsible for measuring the 'inverted voltage'. The join both ADC inputs, but add diodes in between, so one channel works with (+-) and the other channel works with (-+) and then 'merge' the input from both channels using code. Then I should be able to measure things like sin wave for example (where polarities switch).   Is the concept correct or is there a better way to do this? Thanks! In my experience, input type="text" onchange event usually occurs only after you leave (blur) the control.  Is there a way to force browser to trigger onchange every time textfield content changes? If not, what is the most elegant way to track this “manually”?  Using onkey* events is not reliable, since you can right-click the field and choose Paste, and this will change the field without any keyboard input.  Is setTimeout the only way?.. Ugly :-) One part of the render layer glowing? How do I recover my password in Pokemon Go? How to parse hundred html source code files in shell? Will $\sum^{\infty}_{n=1}|a_n|^p$ converge? Given that $\sum^{\infty}_{n=1} a_n^2$ converges,then, will $$\sum^{\infty}_{n=1}|a_n|^p$$ converge for $p&gt;2$?  I couldn't find a counterexample neither a proof but it looks to me that this is true. For $p=3/2$, I found the counter example $\sum a_n=\displaystyle \sum^{\infty}_{n=1} \frac{1}{n^{2/3}}$ Why do popular but not ideal questions keep being closed? I notice a really worrying trend of some really popular questions being closed and eventually deleted. Some of them became legends already, like this one  ? Yes, it does not fit the format ideally, but what is point of obeying the letter of the law to such extent that it becomes ridiculous? Ok, closing is fine if community leaders became so pedantic, but why go so far as to even delete it? At this point it looks like burning old pictures just because you don't like them.  Update: Summary  For now I heard only two clear arguments:   Those questions pollute search results.  Those questions don't play well with enforcing question and answer standards.   Both of that statements are easily verifiable and to my experience are just false. Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$ Why is unity feedback used? The question is:     Show that there are an infinite number of pairs $(m,n): m, n \in \mathbb{Z}^{+}$, such that: $$\frac{m+1}{n}+\frac{n+1}{m} \in \mathbb{Z}^{+}$$   I started off approaching this problem by examining the fact that whenever the expression was a positive integer, the following must be true:  $$\frac{m+1}{n}+\frac{n+1}{m} - \left\lfloor\frac{m+1}{n}+\frac{n+1}{m}\right\rfloor = 0$$  However, I was unable to do much more with this expression, so I abandoned it and started the problem again from a different angle.  Next I re-arranged the expression to state that:  $$\frac{m^2+m+n^2+n}{mn} \in \mathbb{Z}^{+} \implies \frac{m(m+1) + n(n+1)}{mn} \in \mathbb{Z}^{+}$$  And therefore:  $$mn \mid (m(m+1) + n(n+1))$$  However, I'm unsure how to demonstrate there are infinitely many occurances of $(m, n)$ for which this is true. So I'd appreciate any help.   Thanks in advance Basically this suggestion for the Android app:   Many times I'll see that a post has been edited on the Android app. I'll want to see exactly what was edited, and the Android app doesn't show this. Can the revision history be added to the Android app?