When I have to decide whether a clause is restrictive/non-restrictive I typically figure out whether the information in the restrictive clause is, in my opinion, necessary. Is this correct or is the fundamental definition that the sentence would grammatically be incomplete without the restrictive clause. I saw some examples where the sentence would be complete without the corresponding restrictive clause, but would like to have a definite answer. Example sentence is:      Would you lend me the video that you told me about last month?   In my understanding, the sentence would be grammatically correct without the restrictive clause ("would you lend me the video?"), and thus, the definition of a restrictive clause depends on the writers judgment!  Thank you!
Can you tell me the difference in the meaning of the two sentences below?  As a defining relative clause.     The location which was called Central Park was a park in New York.    As a non-defining relative clause.     The location, which was called Central Park, was a park in New York.
How to check if file exists on FTP before FtpWebRequest I have a bit of a unique problem. Well, maybe not a problem because I'm really just curious about it, but...  I have a simple 8 digit calculator. It has +, -, x, /, and a constant operation function. It has no usable memory slot.  I need (lit. would like to know how) to calculate ln(x) on this calculator. Any series I have found lose a lot of precision since whatever is outside the 8 digit range is truncated without rounding. I have used Padé approximants with trig functions, and a continued fraction for exp(), but none of these two methods are adequate for ln(x), either because there is no way around the truncation error or it requires writing down many intermediate values, or it requires memorizing and punching in many constants.  Does anyone know any good way to calculate ln(x) (or any other base, since memorizing one constant is OK) to as many digits as possible as easily as possible on this calculator (bonus points to methods where the value on the screen is immediately, meaning you don't need to write it down)?  For that matter, if you happen to know some good ways to calculate other special functions, I am interested in that as well.  Thanks! difference between accuracy and Rand index (R) I'm very confused, when I read on the wikipedia "From a mathematical standpoint, Rand index is related to the accuracy, but is applicable even when class labels are not used."   and   But when I use in R the rand.index function from fossil package and the Accuracy function from MLmetrics it doesn't give the same answer  &gt; Accuracy(predicted, real) [1] 0.8266667  &gt; rand.index(predicted,real) [1] 0.7114989  Please can someone explain to me the difference between these two and which one should I use?  NB:I use the k-medoids clustering algorithm (function pam from cluster package) When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric , which is inversely proportional to the radius in the case of a single point charge (all field lines are directed radially).   My question may sound dumb, despite the fact that this concept is quite intuitive, but if you think about it there is actually an infinite amount of field lines which we can draw everywhere (one through every point), so speaking of an area where field lines are more "dense" or "sparse" doesn't make much sense to me.  With this in mind, why can we still use such a concept? Why does it really work? Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$ Let $m,n$ be two integers such that, $m\ge n$. Compute the number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$   There are $n^m$ functions (total).  we subtract from $n^m$ the number of non-surjective functions.  There are $\binom{n}{1}(n-1)^m$ functions missing one element.  There are $\binom{n}{2}(n-2)^m$ functions missing two elements, but how many times did we count this in the previous count ?  Then we have to add this again by inclusion-exclusion but why is the difference always 1? Show that $\ker \hat{T} = \text{ann}(\text{range } T)$ This is an old exam problem: Let $V$ and $W$ be finite dimensional vector spaces over a field $F$ and let $T: V \to W$ be a linear transformation. Define $\hat{T}: W^* \to V^*$ by $(\hat{T}(f))(v)=f(T(v))$. Here, $U^*$ denotes the dual vector space $U$. Since $\hat{T}$ is a linear transformation prove $\ker \hat{T} = \text{ann}(\text{range } T)$ where $\text{ann}(Y) = \{g \in U^* : g(y)=0 \text{ for all } y \in Y \}$ for a subspace $Y$ of vector space $U$.  I'm really not sure how to start this problem. Any advice would be great! Trigger a button click with JavaScript on the Enter key in a text box I've read some great on-topic example questions on Area 51.  My questions:   Should a proposed site's "Great On-Topic Example" questions be automatically included in its beta? Will a proposed site's "Great On-Topic Example" questions be automatically included in its beta? How do I choose grid and block dimensions for CUDA kernels? Is it possible to trade Pokemon from the 1st generation games to the most recent ones? I know that you can trade Pokemon between games of the same generation (Gold/Silver, Ruby/Sapphire) and even trade between 1st gen and 2nd gen. However, I haven't been able to find a way to trade Pokemon so that I can play with my 1st generation Pokemon in HeartGold, for instance. If it is possible, how many steps would it take and what equipment would I need? Pressure and weight? (hydrostatic paradox) Consider two different shaped containers having same area: one is cylinder, the other is like an inverted pyramid (roughly). Both have the same level of water, the weight of the inverted pyramidal container will therefore be greater than that of the cylinder. But I know from Pascal's law that the pressure should be same in both containers. If the base areas are the same then the force (weight as measured by a scale) should also be the same. Why are the weights different? My Alt + Tab menu looks and works oddly Travelling on Business visa to UK for tourism purposes Currently I am using Outlook 2010, and sometimes customers claim that they will received an attachment in Windows.dat format.  I have searched online for possible solutions, but mostly the suggestion is to change the sending format to plain text. However, by using plain text format, there is some limitation.  So I just wonder, besides the plain text format, is there a ways to solve the winmail.dat issue?  Besides, does plain text format really 100% avoid the issue? Is time dilation an illusion? It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and never goes faster regardless of the direction of relative motion,  the clocks on earth should register less time than the clock on the spaceship.  Is this true? Whenever there is a fast-moving object such as a rocket do all clocks on earth really become slow?  If the rocket with the clock landed after moving at relativistic speed, would its clock and the earth's clock again show the same time since during its travel both appeared slow to each other?  Or is all this just an illusion, ie. the clocks just appear to be slow to each other but in actually run at normal speed, and neither is behind when the rocket actually lands? It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? "Speak to" vs. "Speak with" What are the differences between these two phrasal verbs and what are the best situations to use each? How to type \sim above another symbol x? I want to put a "~" above x, just like \hat x but replacing \hat with \sim.   How to do that? Since the Earth has a magnetic field, can it, in theory, be run through a conductive metal coil to create electricity? Exporting QGIS contour attributes in DXF file? I have a .tiff data file that generates contours in QGIS. I save it as .dxf. The contours don't have any attributes or data. That's bad, because I want to make a 3D landscape in Revit using the information.   How do a save/export the contour lines from QGIS so that they have a z-elevation attribute or at least some information?    I ticked the attributes box when extracting the contours, but the attributes doesn't show in the dxf.