An exception with == vs is?
Is there a difference between "==" and "is"?
Classifying whether a collection of objects is a set I'm wondering whether or not there is a definite criterion for determining whether a collection of objects is a set. In the literature, I've recently encountered some obscure examples (in Riemann Surface Theory, to be precise) of naturally-arising collections of objects which are not sets.   Here is some pseudo-rigor to make the question more precise:   Let $S$ be a collection of objects. Is there some property $P$ so that $S$ is a set iff $S$ has property $P$? Can I delete unnecessary device simulators of Xcode? I found that Xcode on my laptop consumes much of its storage, so I am trying to delete unnecessary files in Xcode.  There are four directories under Application/Xcode.app/Contents/Developer/Platforms/. I feel that WatchSimulator.platform and AppleTVSimulator.platform are not necessary, because I use Xcode almost only for basic iOS development.  I would like to know if I can delete those platforms directories directly? Why “which” returns none on some commands I can run? Use (or non-use) of articles before abstract nouns Different dependencies for different build profiles Is it possible to have a different set of dependencies in a maven pom.xml file for different profiles?  e.g.  mvn -P debug mvn -P release   I'd like to pick up a different dependency jar file in one profile that has the same class names and different implementations of the same interfaces. Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$ Evaluation of $\displaystyle \int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$   $\bf{My\; Try::}$ Let $\displaystyle I = \int_{0}^{1}\frac{x\ln x}{\sqrt{1-x^2}}dx\;,$ Put $x=\cos \phi\;,$ Then $dx = -\sin \phi d\phi$  and Changing Limit, We get  $$\displaystyle I = -\int_{\frac{\pi}{2}}^{0}\cos \phi \cdot \ln(\cos \phi )d\phi = \int_{0}^{\frac{\pi}{2}} \ln(\cos \phi)\cdot \cos \phi d\phi$$  Now Using Integration by parts, We get  $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{\sin^2 \phi}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{(1-\cos^2 \phi)}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\sec \phi d\phi-\int_{0}^{\frac{\pi}{2}}\cos \phi d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-\left[\sin \phi\right]_{0}^{\frac{\pi}{2}}$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-1$$  Now How can I solve after that, Help Required, Thanks How do I get the  value of a character as an int in ? I am using ArcMap 10.2 and want to represent a layer in a rotated dataframe with chart (graph) symbology. The problem is that the charts do not rotate with the dataframe:     I thought I could convert to graphics and rotate each chart individually, but   that is very tedious I don't find an option to convert a layer to graphics, works for the legend but not for the actual layer symbology Prevent Word from Including Bullet Letter when Copying Text I'm copying quite a bit of text from Word into a text-based application, line by line.  The word text is structured like this:        Topic      a. Item A      b. Item B      When I highlight Item A, copy, and then paste into the text-based application, I get a.    Item A rather than just Item A as desired.  How can I prevent Word from including the bullet letter when copying? I'm training a neural network for regression. The input vector consists of $140$ entries.   For each feature vector entry, I calculate both min and max over the training set. The difference max-min of some entries are smaller than 1e-5. I understand I can normalize such feature entries by say MinMaxScalar. However, if the difference max-min is this small, can I discard such entries since they seem to be so insensitive? I have a simple question answer to which would help me more deeply understand the concept of (non)commutative structures. Let's take for example (our teacher's definition of) a ring:  Let $R\neq \emptyset$ be a set, let $\oplus:A\times A \to A$ and $\bullet :A\times A \to A$ be binary operations. Moreover, let $(R, \oplus)$ be a commutative group, $(R, \bullet)$ be a monoid and following property holds for all $a, b, c\in R$: $$a\bullet(b\oplus c) = (a\bullet b)\oplus(a \bullet c)$$ $$(b\oplus c)\bullet a = (b\bullet a)\oplus(c \bullet a)$$ Then ordered triple $\mathbf R = (R, \oplus, \bullet \mathbf)$ is called a (unitary) ring.  Moreover, we call ring $\mathbf R$ commutative iff $(R, \bullet)$ is a commutative monoid. Commutativity of a ring is always a matter of its multiplicative operation because the additive operation is always assumed to be commutative.  Could anyone explain me the bold part? Why do we even in non-commutative rings (and fields etc.) assume the addition to be always commutative? Is there some serious reason? Would it make any trouble? Or studying of structures with non-commutative addition just doesn't give us anything new so we can take addition as commutative simply because of our comfort? Splitting a semicolon-separated string to a dictionary, in Python Loading .sql files from within PHP I have a directory on my Windows 7 machine that has hundreds if not thousands of sub-directories.  Some of them have files, some do not.  I want to delete all the empty directories.  Looking at the del and rmdir DOS command, it does not look like you can recursively do this without deleting all the files.  Is there a way to do this from the command line? RGB and CMYK: Why both? Any of you who have at least little experience with graphic design software, photography or professional printing, must have -almost undoubtedly- have gone through this: 'the struggle' of RGB and CMYK colour spaces.  Now, there are many questions regarding matters of 'which should I choose', 'what is what' and converting problems, but that's not really what I'm after here.  As a graphic designer with only a couple of years of experience, I still have this struggle from time, and find the whole CMYK/RGB choosing/converting/saving situation quite confusing, to say the least. I do know that RGB is meant for digital end purposes, and CMYK is suitable for printing.  I have always been wondering about the neccesity of this whole thing. So, my question is: why are there these two colour profiles, instead of just having one?   Wouldn't it be a lot easier if printers or software could convert any RGB file to a CMYK printing document instead? I'm pretty sure it does already exist, by the way, because printing an RGB file sometimes simply prints the right colours for me. Alas, not always (doesn't seem to be related to the printer of software I print from).    I have gone trough some RGB vs. CMYK-related questions and found this, a.o., (), an answer of user DKuntz2 (thanks DKuntz2):     RGB is a light-based theory. All colors begin with black "darkness",   to which different color "lights" are added to produce visible colors.   RGB "maxes" at white, which is the equivalent of having all "lights"   on at full brightness (red, green, blue).      CMYK is a color-based theory. All colors start with white "paper", to   which different color "inks" are added to produce output colors. CMYK   "maxes" at black, at which point all "inks" are applied at 100% (cyan,   magenta, yellow, black).   Not sure if this is entirely right, though, because some people disagreed with DKuntz2:     I disagree. With RGB you start with black - the absence of light; with   CMYK you start with white paper.   – e100  Although this does clarify the differences fairly well, I still don't see the point of the two colour profiles(/spaces)    Side question: What happens when you work in an RGB document in photoshop, then press ctrl+y? Photoshop says the document is RGB/8/CMYK, but it can't be both. Right?  EDIT:  Big thanks for the answers, the (current) three below are very informative and interesting. I understand the whole thing a bit better, although it's all very complicated and in-depth to me. Especially when I read about terms like colour models, colour profiles, colour spaces, colour spectra and gamut all one after another.  As much as I would like to accept an answer as the desired one, I feel that my question in the core isn't fully answered yet. What I would really like to emphasize is what I asked about earlier: Wouldn't it be a lot easier if printers or software could convert any RGB file to a CMYK printing document instead?. As Alan Gilbertson explained, the reason is - if I understand correctly - basically a 'lost-in-translation' thing that makes the conversion not 100% accurate, and the colours to possibly be a bit distorted.  However, I still don't see how the solution cannot be an automated conversion done by a printer. Should be possible with modern technology; if you can convert RGB to CMYK in Photoshop, why can't a printer do the exact same for you? As was also said in the answers, the slightest differences in colours and colour spaces, can not be seen by the human eye. And that's what it all comes down to: what we want to see. Be it on a screen or on a sheet of paper.  The fact that this question has three very long answers, or even moreso the fact that there are so many questions about these two colour models (I now know the right term, yay) kind of proves that this is way more complicated than it should be. How to add an edge ring around a hole What is the easiest way to add/extrude an edge loop around the hole in the first image to make it like the second image? How can I match a quote-delimited string with a regex? If I'm trying to match a quote-delimited string with a regex, which of the following is "better" (where "better" means both more efficient and less likely to do something unexpected):  /"[^"]+"/ # match quote, then everything that's not a quote, then a quote   or  /".+?"/   # match quote, then *anything* (non-greedy), then a quote   Assume for this question that empty strings (i.e. "") are not an issue. It seems to me (no regex newbie, but certainly no expert) that these will be equivalent.   Update: Upon reflection, I think changing the + characters to * will handle empty strings correctly anyway. Double integral of an function odd with respect to $y$ over a domain symmetric with respect to $x$ axis Let $D$ be a region given as the set of $(x, y)$ with $$a \leq x \leq b\quad\text{and}\quad-\Phi(x) \leq y \leq \Phi(x)$$ where $Φ$ is a nonnegative continuous function on the interval $[a, b]$.  Let $f(x, y)$ be a function on $D$ such that $$f(x, y) = - f(x, - y)$$ for all $(x , y) \in D$.  Argue that $$\displaystyle \iint_D f(x, y) dA = 0.$$ I was recently asked to find the accumulation points of the set $$S = \{(-1)^n + \frac{1}{n} \mid n \in \mathbb{N}\}$$  I answered that the accumulation points are $\{-1,1\}$, because despite the fact that $\frac{1}{n}$ diverges, we can still use $\frac{1}{n}$ to find an element arbitrarily close to either $1$ or $-1$, i.e. to show that there is an element in an arbitrarily small neighborhood of $1$ or $-1$. (No proof was required for this question --- this is my intuition.)  Am I right at all? Which way does the scale tip?