Converse of Lagranges theorem question:
Why is the Converse to Lagrange's Theorem False?
Error "Power::infy: Infinite expression 1/0 encountered". Why do I get this? What are the various physical mechanisms for energy transfer to the photon during blackbody emission? How do levers amplify forces? This is really bothering me for a long time, because the math is easy to do, but it's still unintuitive for me.  I understand the "law of the lever" and I can do the math and use the torques, or conservation of energy. or whatever... And I can see that a lever can amplify a force you apply to it  if you apply a force on the longer side of the beam.  If I were to look at the molecular lever and see what actually happens when I push on the lever, and I give acceleration to the molecules, how does it actually happen that more force is transmitted to the other side?  Thank you all  p.s I'm looking just for an explanation in terms of forces and acceleration, it's clear to me how to do this in terms of energy or torques Lightning Web Component embedded in Visualforce Page via Aura Component and App not displaying I am writing a lightning web component that is going to be used in Salesforce Classic, Lightning Experience and an Employee Community. It does not HAVE to be a lightning web component - I could use a traditional Aura Lightning Component if I must.   However, what I am finding is that the visualforce page does not work, even when the lwc component is embedded in a aura component that is then used with Lightning Components for Visualforce. I can see from the documentation  that using a lwc directly from within visualforce is not supported, but I was under the impression that it may work if wrapped in an aura component.   My question then is this:  Has anyone had success having a lwc wrapped in an aura component display successfully within Visualforce? Or is this completely unsupported behaviour? It is a common practice to apply PCA (principal component analysis) before a clustering algorithm (such as k-means). It is believed that it improves the clustering results in practice (noise reduction).   However I am interested in a comparative and in-depth study of the relationship between PCA and k-means. For example, Chris Ding and Xiaofeng He, 2004,  showed that "principal components are the continuous solutions to the discrete cluster membership indicators for K-means clustering". However, I have hard time understanding this paper, and Wikipedia actually .  Also, the results of the two methods are somewhat different in the sense that PCA helps to reduce the number of "features" while preserving the variance, whereas clustering reduces the number of "data-points" by summarizing several points by their expectations/means (in the case of k-means). So if the dataset consists in $N$ points with $T$ features each, PCA aims at compressing the $T$ features whereas clustering aims at compressing the $N$ data-points.  I am looking for a layman explanation of the relations between these two techniques + some more technical papers relating the two techniques. How can you programmatically tell an HTML SELECT to drop down (for example, due to mouseover)? Does "it is entirely possible that" require the subjunctive form of the verb following "that"? Prove that for every $n\geq m \geq1$ natural numbers, the following number is an integer:  $${\gcd(n,m)\over n}\cdot{n\choose m}$$  Where $\gcd$ is the greatest common divisor.  I tried to make it simpler by cancelling the $n$ from the left side, and making it $(n-1)!$ on the right: $\gcd(n, m) \cdot \frac{(n-1)!}{m!(n-m)!}$, but can't really go further.   This was problem B-2 on the . I am not sure which conjunction to use in the following context:        I know about programming but I have a little bit of confusion in Java programming.   I know about programming although I have a little bit of confusion in programming.    I know about programming however I have a little bit of confusion in Java programming. How to increase ping time/network connection latency on Windows? I need to permanently increase network latency in approximately 100ms, without losing packets.  Reason: On a certain server and internet game my ping is too much lower than the other people playing it. I have 15ms, when average is 150ms which gives me cheater-like advantages.  So also out of curiosity I'm looking for ways to increase my ping while keeping connection stable. What are my options if any?  I thought about VPN services, but it seems like a bad option since games use UDP?  Is there any router/software that would assist me on this?  I'm on windows. Why can't I suggest edits on SE meta sites? When you click &quot;edit&quot; on a meta site as a non-edit-privileged user, the error message appears:  Suggested edits are not allowed on non-tag-wiki posts on meta sites.  Right as I was going to post this as a possible bug, I finally found  which says that per-site Metas don't have suggested edits by-design because it's &quot;not needed&quot;. However, I've been participating a lot over at  where there is a lot still to be figured out in terms of site guidelines.  The Meta is one of the most active I've seen and a lot of the questions are really trying to gather community-built suggestions.  So maybe more of those need to be Community Wiki, but it still brings me to ask why don't per-site-metas &quot;need&quot; suggested edits? Adding bounty: The more betas I participate in, the more I don't get this. I've been using gksudo nautilus and sudo nautilus through Alt+F2.   What's the difference? They look very similar! Divergent or not series? How tipe are this series?  $$\sum_{n=2}^\infty \frac 1 {n^2\ln n}$$ But $$\sum_{n=2}^\infty \frac 1 {n\ln n\ln(\ln n)}$$ I used Condensation Test, but I stack after that. Thanks! Evaluation of $\lim_{n\rightarrow \infty}\frac{1}{2n}\cdot \ln \binom{2n}{n}$ I'm just getting started with Pinter's A Book of Abstract Algebra, please be kind. The book solution for Chapter 2, Problem 7 claims that the following operator is non-associative:  $$ x * y = \frac{xy}{x+y+1}$$  The book solution:  $$ (x * y) * z = \left(\frac{xy}{x+y+1}\right) * z = \frac{xyz(x+y+1)}{x+y+z+xy+yz+xz+1}$$  $$ x * (y * z) = x * \left(\frac{yz}{y+z+1}\right) = \frac{xyz(y+z+1)}{x+y+z+xy+yz+xz+1}$$  However the $(x+y+1)$ and $(y+z+1)$ terms appear to actually cancel out:  $$ (x * y) * z = \left(\frac{xy}{x+y+1}\right) * z = \frac{\left(\frac{xy}{x+y+1}\right)z}{\frac{xy}{x+y+1} + z + 1} $$  $$ x * (y * z) = x * \left(\frac{yz}{y+z+1}\right)  =\frac{x\left(\frac{yz}{y+z+1}\right)}{x+\frac{yz}{y+z+1} + 1} $$  So the denominators cancel out, the two groupings are equivalent, the operator is associative.  This result is duplicated in Mathematica, but I'd like to make sure I'm not missing something.  Sorry for bothering people with such a basic question. How to send mail from the command line? How to send mail from the command line? What is the difference between a homepage link with or without a trailing slash? Bottom frame of listing appears on top of the next page Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$. How do I define custom web.config sections with potential child elements and attributes for the properties? The web applications I develop often require co-dependent configuration settings and there are also settings that have to change as we move between each of our environments. All our settings are currently simple key-value pairs but it would be useful to create custom config sections so that it is obvious when two values need to change together or when the settings need to change for an environment. What's the best way to create custom config sections and are there any special considerations to make when retrieving the values?