Why is the following relation anti-symmetric?  {(1,2), (2,3), (3,4), (1,4), (1,3), (2,4)}  From my understanding, it is anti-symmetric if:  $$ (a, b) \in R,  (b, a) \in R, b=a $$  Must hold. Which is it this case not true. I would rather say it is asymmetric since there is no symmetric nor anti symmetric relation at all.
Given a set $\{1,2,3,4\}$, how is the following relation $R$ antisymmetric?  $$R = \{(1, 2), (2, 3), (3, 4)\}$$  Note: Antisymmetric is the idea that if $(a,b)$ is in $R$ and $(b,a)$ is in $R$, then $a = b$. In my textbook  it says the above is antisymmetric which isn't the case as whenever $(a,b)$ is in $R$, $(b,a)$ is not.
I'm creating a composite image, in order to create a timeseries. I've already created the composited image, but i am having difficulty masking the clouds of the composite image. I've followed the code from a page having similar problems, however when I run the code (after replacing all the l8_mayo to composite as that is the name of my composite var), I get the error code of composite.map not a function. This error does not come up when I run the exact same code from the previous answer. Can someone explain how to overcome this problem? Here is the page I used:  here is my code and the link to my code:  (point is the long, lat for Lake Manyara, Tanzania)  //load images for composite var sr14= ee.ImageCollection('LANDSAT/LC08/C01/T1_SR') .filterBounds(point) .filterDate('2014-01-01','2014-03-01') .select(['B4','B3','B2']);  // Temporally composite the images with a maximum value function. var composite = sr14.max(); Map.setCenter(35.8244, -3.5799); Map.addLayer(composite, {}, 'max value composite');  var getQABits = function(image, start, end, newName) { // Compute the bits we need to extract. var pattern = 0; for (var i = start; i &lt;= end; i++) {    pattern += Math.pow(2, i); } // Return a single band image of the extracted QA bits, giving the band // a new name. return image.select([0], [newName])               .bitwiseAnd(pattern)               .rightShift(start); };  // A function to mask out cloudy pixels. var cloud_shadows = function(image) { // Select the QA band. var QA = image.select(['BQA']); // Get the internal_cloud_algorithm_flag bit. return getQABits(QA, 7,8, 'Cloud_shadows').eq(1); // Return an image masking out cloudy areas. };  // A function to mask out cloudy pixels. var clouds = function(image) { // Select the QA band. var QA = image.select(['BQA']); // Get the internal_cloud_algorithm_flag bit. return getQABits(QA, 4,4, 'Cloud').eq(0); // Return an image masking out cloudy areas. };  var maskClouds = function(image) { var cs = cloud_shadows(image); var c = clouds(image); image = image.updateMask(cs); return image.updateMask(c); };  var composite_free = composite.map(maskClouds);  Map.addLayer(composite_free, 'composite collection without clouds'); Remove category & tag base from WordPress url - without a plugin Why is the empty set considered an interval? Implicit conversion issue in a ternary condition Adding DC voltages of PSU I need to add two voltages together that share a common ground (power supply from computer). I tried using bridge rectifiers and Op-Amps. Quantify Difference/Distance between Lognormal distributions I am trying to determine a metric that quantifies the distance between two continuous lognormal distributions. The data is actually a mixture of two lognormal distributions (I am not sure if this can be called bimodal). The individual distributions have different means but the same standard deviations. I have 20 data sets that can be divided into 4 groups, with each group having a constant standard deviation, but the 5 data sets in each group are made up of two distributions with different means. Some examples:      I am in search of a metric that accounts for the contrast (difference in means) and the standard deviation. I have tried out some parameters like coefficient of variation (of the mixture), Ashman's D etc. I have also tried percentage of overlap. However the problem always is that, at the end when plotted against the results I end up with 4 trend-lines again, corresponding to the 4 different standard deviations. Is there some other way I can quantify this?  Just to make myself clear, I want to quantify the difference between two distributions in a single case (between the red and green PDFs in the above image). Filling cells with sequential numbers in an Excel (2003) macro I need to fill an excel column with a sequential series, in this case from -500 to 1000.  I've got a macro to do it, but it takes a lot of lines for something that seems like it should be a single function [something like FillRange(A2:A1502, -500, 1000, 1)].  But if that function exists, I can't find it.  Is the following as simple and elegant as it gets?  'Draw X axis scale Cells(1, 1).Value = "mV" Cells(2, 1).Value = -500 Cells(3, 1).Value = -499 Cells(4, 1).Value = -498  Dim selection1 As Range, selection2 As Range  Set selection1 = Sheet1.Range("A2:A4") Set selection2 = Sheet1.Range("A2:A1502")  selection1.AutoFill Destination:=selection2 patching SQL Server with Availability Group and Secondary Replica I am currently writing my bachelor thesis and I am using LyX as my standard writing program (because I am not familiar with LaTeX at all).  For my bibliographystyle I use JabRef and the citation style needs to be Journal of Finance.  Now, I found this .bst file for the Journal of Finance style online () which is actually really good. But the problem is, that I need it in German. There must be an "und" instead of "and" and all the umlauts don't work as well. Basically I need everything in German.  Do you know a website with a German .bst file? Or can I change something in the settings in LyX or JabRef and everything would be fixed? How to create Mist in Blender I already tried several ways to create Mist in Blender, but it never worked 100%. I use Blender 2.78 and I want to create Mist like in this scene here.  What are the exact steps?     Here is what I have tried so far:  I already tried this:  but it simply did not work .. I dont know why.  (EDIT: I managed to fix it: Check out this graphic:   Until now I already used objects successfully as Mist-creators (Volume Scatter under Volume Material). The bad thing about using Objects as Mist-creator is that they dont have an endless mist range + the mist can not be bright. Normally it appears grayish result is bad..  Check it out  Please help If $p,q,r$ are all primes,and $p|qr-1$,$q|pr-1$ and $r|pq-1$,find all possible values of $pqr$. How to disable the keyring for SSH and GPG? Finding the nth non square free number We all know what  numbers are. I was more interested in checking an efficient way to find nth non square free number. Calling a function in main For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? Banach spaces and their unit sphere Let $X$ be a normed vector space.   Show that if a subsequence of a Cauchy sequence converges, then the whole sequence converges. Use the part 1 to show that $S = \{x\in X : \|x\| = 1\}$ is complete if and only if $X$ is Banach.     I have found the first part in a book, but I do not how to prove part 2. Thanx regards Creating all possible line segments between all points using QGIS Questions in titles need to be repeated, why?  To me this pattern seems ridiculous. But I frequently encounter the "not a real question" situation, when I put my question in the title, then the context for that specific question in the 'question body'.     So:  I am to take it that the title is almost completely irrelevant for establishing subsequent question body is asking? I choose my titles to expose the actual question so it need not be repeated below. If questions need to be repeated in the body, could we simply title it "A question, click here and read below" ?   Tagged bug, as I have found this "problem" to be quite reproducible.  Steps to reproduce:   Ask a question with the clear, simple question in the title, and the evidence/context/example in the question body. Await close votes. Let $f$ be increasing on $[a,b]$ and $a < x_1 < \dotsb < x_n < b$. Show that $\sum_{k = 1}^n [f(x_k^+) - f(x_k^-)]\leq f(b^-) - f(a^+)$. What are the criteria for questions to be selected for Hot Network Questions?