Users should be required to leave custom comments when closing a question
Should a user be forced to add a comment when they vote to close?
Is there an idiom for someone who gets what he deserved? Like someone receiving punishment for his evil deeds or someone getting awarded for his good deeds? Is it OK to call a professor by his first name when he/she signs emails by only first name? If a professor in a North American country presents his- or herself by his/her first name in email messages, does this mean that students can refer to him/her by his/her first name? Or is this generally not a good idea, unless the professor has explicitly mentioned that he/she can be referred to by first name? I've noticed that most professors, who prefer to be referred to more formally, do not sign their emails with just their first names, but usually initials or first and last name. Why is $\omega$ the smallest $\infty$? I am comfortable with the different sizes of infinities and Cantor's "diagonal argument" to prove that the set of all subsets of an infinite set has cardinality strictly greater than the set itself. So if we have a set $\Omega$ and $|\Omega| = \aleph_i$, then (assuming continuum hypothesis) the cardinality of $2^{\Omega}$ is $|2^{\Omega}| = \aleph_{i+1} &gt; \aleph_i$ and we have $\aleph_{i+1} = 2^{\aleph_i}$.  I am fine with these argument.  What I don't understand is why should there be a smallest $\infty$? Is there a proof (or) an axiom that there exists a smallest $\infty$ and that this is what we address as "countably infinite"? or to rephrase the question "why can't I find a set whose power set gives us $\mathbb{N}$"?  The reason why I am asking this question is in "some sense" $\aleph_i = \log_2(\aleph_{i+1})$. I do not completely understand why this process should stop when $\aleph_i = \aleph_0$.  (Though coming to think about it I can feel that if I take an infinite set with $\log_2 \aleph_0$ elements I can still put it in one-to-one correspondence with the Natural number set. So Is $\log_2 \aleph_0 = \aleph_0$ (or) am I just confused? If $n \rightarrow \infty$, then $2^n \rightarrow \infty$ faster while $\log (n) \rightarrow \infty$ slower and $\log (\log (n)) \rightarrow \infty$ even slower and $\log(\log(\log (n))) \rightarrow \infty$ even "more" slower and so on).  Is there a clean (and relatively elementary) way to explain this to me?  (I am totally fine if you direct me to some paper (or) webpage. I tried googling but could not find an answer to my question) What is meant by a "random variable"? What do they mean when they say "random variable"? Prove the map has a fixed point Assume $K$ is a compact metric space with metric $\rho$ and $A$ is a map from $K$ to $K$ such that $\rho (Ax,Ay) &lt; \rho(x,y)$ for $x\neq y$. Prove A have a unique fixed point in $K$.  The uniqueness is easy. My problem is to show that there a exist fixed point. $K$ is compact, so every sequence has convergent subsequence. Construct a sequence ${x_n}$ by $x_{n+1}=Ax_{n}$,$\{x_n\}$ has a convergent subsequence $\{ x_{n_k}\}$, but how to show there is a fixed point using $\rho (Ax,Ay) &lt; \rho(x,y)$? Prove that there are no integers $a,b \gt 2$ such that  $a^2{\mid}(b^3 + 1)$ and $b^2{\mid}(a^3 + 1)$. Do AWS Reserved Instances need to be assigned to the instance? I have an RDS instance running of type db.t2.small.  I bought a reserved instance for 1 year of the same type, I paid the partial upfront rate.  Do I need to assign this subscription in some way to my existing instance to say 'This is the instance that is using the subscription' or does AWS just charge for the instance usage depending which instances you have running and whether an available subscription was active for it at the time which determines the running rate?  The reason that I ask is that I can't see any mention of the reduced rate on my AWS Billing area and it shows that I've used 17 hours of my reservation, but there isn't a row on my bill so far this month that indicates the new partial upfront rate that I should be charged for my instance. Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function? Let $a &lt; b$ and $f:[a, b] \rightarrow \mathbb R$ be a Riemann integral function. Suppose that $f(x) \geq 0$ for all $x \in [a, b]$. I want to show whether $\int_a^bf(x) = 0$ implies $f(x) = 0$ or not, but I'm not sure where to start. I don't know much about Riemann integral functions in general. I only know that $$\underline \int_a^b f= \overline \int_a^b f.$$ Also, I know the fact that if $f$ is continuous, then $f(x) = 0$ for all $x\in [a, b]$. Can anyone provide any hints for me, because I'm really confused about this whole thing. What do I use on linux to make a python program executable Duplicate objects transformation applies to both objects I'm facing this frustrating "feature" that I can't seem to remedy; when I duplicate an object (and now, even when I create two completely new objects), their transformations/scaling is synchronized. This is extremely annoying when trying to use any sort of transformation keyboard shortcut.  It should be noted by going to the properties menu (N) and manually setting the properties works just fine.  For instance, here is just the camera selected (trust me, I made sure):   And when I try to transform by clicking+dragging on the X axis OR by hitting G->X, this happens:   They are not grouped (verified by going to the Groups list up in the Scene panel) and they do not have parents (verified by going to Object->Relations).  I have tried the unlink command as well, to no avail.  I have seriously run out of options; what did I change to have my G->X shortcuts transform multiple objects? It seems completely at random, too; certain objects seemed to be "linked" to other random objects, and this "linking" is guaranteed when duplicating even when I do a non-linking duplicate (Shift+D).  What gives? What does it mean for two objects to "touch"? If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of      "I'm not actually touching you! The electrons in the atoms of my   skin are just getting really close to yours!"   Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects.   Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other.  So what does it mean for two objects to touch each other?   Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either?  Is there really no such thing as "touching"? how to properly save an architecture in a fpga ic forever How do I study the "correlation" between a continuous variable and a categorical variable? Programmatical Setting of 'Store Relative Pathways' for multiple MXDs ArcGIS 10.1 I am looking to move large number of mxds to a different location on the same drive. Many mxds haven't got 'Store relative pathways' option checked therefore this operation will result in broken links to data. I've only started using ArcGIS 10.1 and it is now possible to programmatically update relative pathways for all mxds by using arcPy and setting relativePaths to be "True". I had a go at writing Python script which (in theory) loops through a top folder and searches for all mxds and then updates "Store relative pathways" setting to be on. When I run this script in PyScripter, it fails to complete, I get the following error:  "exceptions.NameError: name 'mxd' is not defined  Can anyone help ?!? Thanks in advance, Magda      import arcpy, os  folderPath = r"C:\My Folder Path\...\...\..."  for filename in os.listdir(folderPath):     fullpath = os.path.join(folderPath, filename)     if os.path.isfile(fullpath):         basename, extension = os.path.splitext(fullpath)         if extension.lower() == ".mxd":             mxd = arcpy.mapping.MapDocument(fullpath)             mxd.relativePaths = 'True'         mxd.save() del mxd Beamer and description environment text size I have a issue with my Drupal installation, for example:   when I enable or disable the modules, It redirects me to a blank page, when I create a new content type and save it, redirects me to a blank page, when I add a new view and save it, it redirects me to a blank page, when I try to clear the cache, it redirects me back to a blank page, or in similar cases.   Basically all the confirmation pages redirect me to a white screen. When I refresh it again, it shows me the page. I tried to increase the PHP memory value but it doesn't help.  Are there any other solutions for this?  The error which I'm having:      Fatal error: Allowed memory size of 100663296 bytes exhausted (tried to allocate 8192 bytes) in sites/all/modules/views/plugins/views_plugin_localization_none.inc on line 1 This community wiki explains the current restrictions by the United States of America on the entry of individuals who may pose a risk of transmission of the SARS-Cov2, the virus which causes the Covid-19 disease. How to derive the conjugate prior of an exponential family distribution I am trying to derive the conjugate prior of the univariate Gaussian distribution over both the mean and the precision. I know that the prior I'm looking for is the normal-gamma distribution, but the idea is to derive this result.  It seems that you can write down the conjugate prior of an exponential family distribution immediately if you represent it in the canonical exponential family form.  suggests a way to do just that. So far I have written the Gaussian probability function in this form and equated the following, but I don't see how the form of the conjugate prior is immediately obvious.  $$p(\mu, \lambda | D) \propto p(\mu,\lambda)p(D | \mu, \lambda)$$ Struggling with Plural/Singular? Which of the following is a grammatically correct statement?   The value of cars depreciate over time.   The values of cars depreciate over time. The value of cars depreciates over time.   Thanks! Select first occurring element after another element