what is $e$ really? what is its meaning?
Intuitive Understanding of the constant "$e$"
How can I Remove .DS_Store files from a Git repository? Calculating ratio between "rows" in ArcGIS field calculator I have a problem similar to  but that is for QGIS whereas I have to perform it in ArcGIS. I have to calculate the Ratio between rows (sequentially, i.e., row1/row2, row2/row3 and so on) of a specific field based on the ID field and have to assign the results to a separate field. Here is the code and the error message:  def CalcRatio(ID,Frequency):     vDict = {}     with arcpy.da.SearchCursor(&quot;Test&quot;,['Frequency'],'ID = {}'.format(ID)) as sCur:     for Row in sCur:     vDict[Row[0]]=Row[1] # Dict[id] =Frequency     try: value = ( vDict[1] / vDict[2])     except: value = -1     return value  Message: ERROR 000539: Error running expression: CalcRatio( 1 , 50680) Traceback (most recent call last): File &quot;&lt;expression&gt;&quot;, line 1, in &lt;module&gt; File &quot;&lt;string&gt;&quot;, line 5, in CalcRatio IndexError: tuple index out of range  Here is the data OID Id  Frequency 0   1   50680 1   2   49740 2   3   48620 3   4   48300 4   5   48004 5   6   45600 6   7   44384 7   8   42720 8   9   41890 9   10  39700 10  11  38530 11  12  38207 12  13  38106 13  14  37303 14  15  37205 15  16  36527 16  17  35301 17  18  31674 18  19  28890 19  20  24612 how to remove object from NSDictionary Preserving order with LINQ I use LINQ to Objects instructions on an ordered array.  Which operations shouldn't I do to be sure the order of the array is not changed? In Elias Stein and Rami Shakarchi's Complex Analysis textbook, we have the following exercise:     Show that if $\{a_n\}_{n=0}^\infty$ is a sequence of complex numbers such that $$\lim_{n\to\infty}\frac{|a_{n+1}|}{|a_n|}=L,$$ then $$\lim_{n\to\infty}|a_n|^{1/n}=L.$$    I've been trying to prove this with no luck. The only thing I've thought of doing is $$\lim_{n\to\infty}\left(\frac{|a_{n+1}|^n}{|a_n|^n}\right)^{1/n},$$but this hasn't lead me anywhere except dead ends. Will someone provide a hint for me about how to proceed? Thanks!  Minor update: I don't know if it's helpful yet, but I know we can write the limit as $$\lim_{n\to\infty}\left(\frac{|a_{n+1}a_n\cdots a_0|}{|a_n\cdots a_0|}\cdot\frac{1}{|a_n|}\right).$$This reminds me a lot of the geometric mean, which even has the exponents I'm trying to get... Over the years I've written some libraries. These libraries sometimes depend on each other.  As a result, the "tex" directory is structured as follows:  tex ├── library |   ├── library1.sty |   ├── library2.sty |   └── library3.sty ├── project1 |   ├── master.tex |   ├── chapter1.tex |   └── chapter2.tex ├── project2 |   └── article.tex └── project3     └── paper.tex   The libraries depend on each other. As a result, in every library that depends on another library, this is part of the header:  %library2.sty \ProvidesPackage{library2} \RequirePackage{../library/library1}   In other words, the library is imported from the "root of every project". This is not a good design choice. What if someone copies the libraries in the folder of the root of a project, or what if the folder "library" is renamed...  It is however reasonable the "active directory" still remains in the project root.  What can be done to resolve such library dependencies? Could Hermione really free the Hogwarts house-elves with her knitted hats? Line/word wrapping in revision history and responses tab (and probably other places) and        ()   I just noticed that change. I didn't find new reports under .  Note the names and badge count in the first screenshot, and the badge count in the second one.  PS I can't link to the responses tab as it shows only to the profile owner. When to use an interface instead of an abstract class and vice versa? Can matter really fall through an event horizon? Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$. I want to prove that:  $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$. Fibonacci Recurrence Relations Solve the recurrence relation $f(n) = f(n − 1) + f(n − 2)$ with initial conditions $f(0)=1$, $f(1)=2.$   So I understand that it grows exponentially so $f(n) = r^n$ for some fixed $r$.  This means substituting this $r^n = r^n-1 + r^n-2$ which gives the characteristic equation of $r ^ 2 - r - 1 = 0$. I'm not 100% sure where to move on from here. removeClass and fade animation Does infinity exist in physical systems? Sometimes people fail at asking a question by being too broad, unclear like . So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:     Does infinity exist in either terms of structure, parameters, or   measurement in any physical systems?   Can infinity have any real connection with reality?  Or is infinity purely a mathematical concept just used by physicists as a convenient way to describe the very large, an approximation?  I have heard that if you model a physical system (), and you run into infinity as a solution, then you have either made an error in your calculations or your model is wrong. Does the sequence $\{\sin^n(n)\}$ converge?   Does the series $\sum\limits_{n=1}^\infty \sin^n(n)$ converge? Why doesn't running "sudo shutdown now" shut down? Difference in meaning of "frustrated at" and "frustrated with" What is the difference in meaning of "frustrated at" and "frustrated with" used in sentences like     He is frustrated with me   or      He is frustrated at me   When is each of these sentences above are used? How to change the voltage polarity in an inverting amplifier? I want to implement a simple circuit which can map -10V  +10V voltage range to 0V 5V voltage range. Thus I'm planning to use two op-Amps, one for the slope and the other for the offset. So basically I'm planning to use an inverting amplifier and a summing amplifier consecutively.  But Inverting amplifiers multiplies the input voltage with a minus sign. I need a positive slope. How can I overcome this?  Also Could you gibe me any ideas for a cheap op-Amp models for this purpose? In the example below, an error is caused by \begin{align} and \end{align} but I do not see why:  \documentclass{book} \usepackage{amsmath} \newenvironment{subalign}{\begin{subequations}\begin{align}}{\end{align}\end{subequations}} \begin{document} \begin{subalign}      a&amp;=b\\     &amp;=b \end{subalign} \end{document} Need help with proof for Dedekind cuts on $\mathbb{Q}^+$ I am working on a proof about Dedekind cuts on the positive rational numbers. I have been stuck for a while on the following point and would appreciate any help.  Given $x\in \mathbb{Q}^+$ such that $x^2&lt;2$, how to find $y\in \mathbb{Q}^+$ such $y&gt;x$ and $y^2&lt;2$?