Technical reasons behind formatting when incrementing by 1 in a 'for' loop?
Is there a technical reason to use > (<) instead of != when incrementing by 1 in a 'for' loop?
I have the following validation rule:  AND(  $Profile.Name &lt;&gt; 'System Administrator',  OR(  ISPICKVAL(PRIORVALUE(Level__c), "Archived"),  ISPICKVAL(PRIORVALUE(Level__c), "Closed")  )  )   This validation rule is on the opportunity object, and what I want to achieve is, if the picklist Level__c is either set to Archived or Closed, the opportunity record can only be edited by the System Administrator.  For some reason though, the validation rule also triggers, when I want to set the Level__c to Archived or Closed. But this is not what I want.   Any idea what's wrong with the validation rule? Let $({\Bbb R},{\mathcal A},\mu)$ be the measure space where ${\mu}$ is the Lebesgue measure.  Assume that $\int_{\Bbb R}|f|^pd\mu&lt;\infty$ ($p\geq1$). There is an exercise for proving that       $$\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s).$$   If one formally let $s=t^p$, then $ds=pt^{p-1}dt$ and one would immediately get the equality above. However, how can I justify it rigorously in the sense of Lebesgue integration?    [Edited] What puzzles me is that I have the "change of variable" theorem for Riemann integration, but all the integrations here are in the Lebesgue sense. Unless one has shown that the integrands are also Riemann integrable, how can I directly use "change of variable"? I want to block Facebook (the Facebook site) for concentrating purposes, but I don't want to break the share or like buttons on other pages (like a good article or a nice clip on YouTube I want to like or share). How can I do that? I use both Windows and Linux. I have a directory where daily subdirectories are created, literally named according to $date. How can I delete folders and their contents that are older than 7 days according to the YYYYMMDD in the file name and not the metadata date? Say I have (skipped some for brevity):  20170817 20170823 20170828 20170901   I would end up with the following folders (which those should keep):  20170828 20170901   I created a variable that holds the date 7 days ago: dt_prev=$(date -d "`date`-7days" +%Y%m%d)  My thought was to ls -l a list of these folder names and compare row by row, but this involves cleaning that list, etc., and I figure there has to be an easier way. Are all n-ary operators simply compositions of binary operators? Take for example $A \times B \cdot C$ = $(A \times B) \cdot C$ where $A, B, C$ are 3-component real vectors.  We can define a 3-nary operator $\times - \cdot$ that is a composition of the two common binary operators $\times$ and $\cdot$.  The same thing happens with most functions (operators) - the way we calculate them is by doing smaller binary problems and adding together.  Every time I try to come up with an $(n &gt; 2)$-ary operator my mind automatically looks for binary operators.  So, the question is, do there exist operators (of some weird kind in some branch of math) that cannot be decomposed into 2-ary and 1-ary operators?  Thanks. Why is $\sqrt{-x}*\sqrt{-x}=-x?$ Q1 - Why is $\sqrt{-x}*\sqrt{-x}=-x?$  Q2 - I was thinking it would be:  $\sqrt{-x}*\sqrt{-x}=\sqrt{-x*-x}=\sqrt{x^2}$ but apparently not (why not?)  Q3 - What are the formal algebra rules to use? Can I calculate this without using i such as in: $\sqrt{-x}*\sqrt{-x}=i\sqrt{x}*i\sqrt{x}=-\sqrt{x^2}=-x$. Polynomials vanishing on an infinite set I'd like some help making this argument complete and rigorous (if it's correct - if not, help with that would be nice).  Here $k$ is a field.     Let $A_1,\ldots,A_n \subseteq k$ be infinite subsets. Then any polynomial in $k[x_1,\ldots,x_n]$ that vanishes on $A_1\times\cdots\times A_n\subseteq k^n$ must be $0$ (as a polynomial).   This is what I have ...  For the case $n=1$, a non-constant polynomial can only have as many roots as its degree, and in particular, it must have a finite number of roots. The only polynomial in one variable that has an infinite number of roots is $0$, so if a polynomial in $k[x_1,\ldots,x_n]$ vanishes on an infinite subset then it must be $0$.  For the inductive step, suppose the proposition is true for less than $n$ subsets and variables. Let $p\in k[x_1,\ldots,x_n]$ vanish on $A_1\times\cdots\times A_n$. Fix $x_n$ as some $a\in A_n$, and we have a polynomial in $n-1$ variables that vanishes on the set $A_1\times\cdots\times A_{n-1}$, so by the inductive hypothesis it must be identically $0$.  (Now it gets sketchy). Since this is true for any of the infinite values in $A_n$, and , $p$ must be $0$. How much money does Stack Exchange make? Equivalent of "both" when referring to three or more items? What would be the correct word to use when referring to three or more items, in the same manner as the word both?  For example, using two words, with the word both:     "There are several recommendations I   have to further improve the sites —   both to improve their profit, and   decrease their cost."   Using three words, with a blank space in place of the correct word:     "There are several recommendations I   have to further improve the sites —   _ to improve their profit, decrease their cost and improve their   usability."   So, what would be the correct word to use in place of the __? Is there any short way to save the pipe output to the same file that it's processed. For example, this is what I am actually doing  $ cat filename | sort | uniq &gt; result $ rm -f filename $ mv result filename   I was wondering if there was a way to do it in just one line (not appending those commands using &amp;&amp;)  This is not the way, but to get an idea  $ cat filename | sort | uniq &gt; filename My laptop is filled with viruses and Windows XP is just becoming impossible to work with.   I've been interested in Ubuntu for a while, so, would I be able to use something like Debian to clear my HDD and OS and then install Ubuntu and start fresh? Prove: If a sequence converges, then every subsequence converges to the same limit. For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$ For a polynomial $p(z)=a_0+\ldots+a_nz^n$, prove there exist $R&gt;0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$.  I get $|p(z)|\geq |a_n|R^n$, which makes that factor of $1/2$ useless. So I must have done something wrong.  $$|\frac{\partial^n{f}}{\partial z^n}(P)|\leq \frac{\sup_{z\in \overline{D}(P,r)} |f(z)|k!}{r^k}$$. This is the Cauchy estimate.   $$|\frac{\partial^n{p}}{\partial z^n}(z)| = |a_n n!|$$ $$|\frac{\partial^n{p}}{\partial z^n}(0)|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|n!/R^n$$ $$|a_n n!|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|n!/R^n$$ $$R^n |a_n|\leq \sup_{\zeta\in \overline{D}(0,|z|)} |p(\zeta)|$$  There exist a $z_0$, such that $|z_0|&gt;0$ and $$\sup_{\zeta\in \overline{D}(0,|z_0|)} |p(\zeta)| = |p(z_0)|$$.  This is saying there exist a disk centered at the origin, such that $|p|$ is maximum on some point on the boundary.   Let $R=|z_0|$, we have $R^n |a_n|\leq |p(z_0)|$  Edit: I know what I got wrong. $z_0$ is just one point on the circle $|z| = R$. One can chose another point $z_1$ on the circle, such that $p(z_1)&lt;p(z_0)$. Is it possible to assign numbers generated in an Error-Message? Make Chrome always execute with flags, for eg., directly opening an HTML file I want to run Chrome with a given set of flags, always  I created a shortcut and added the flag to it in the following way, so my target of the shortcut says:  C:\&lt;application-path&gt;\chrome.exe --user-data-dir=D:\Chrome   But when I double click an HTML file, or if any other application triggers Chrome, it looses the flag value. The result - A new chrome window opens with Default profile directory.  I want to make the flag permanent, so that its active irrespective of however Chrome executes.  I tried changing the following registry key:  HKEY_CLASSES_ROOT\ChromeHTML\shell\open\command   It was this earlier:  "C:\&lt;application-path&gt;\chrome.exe" -- "%1"    I changed to following attempts which did not work:  1. "C:\&lt;application-path&gt;\chrome.exe" -- "%1" --user-data-dir=D:\Chrome 2. "C:\&lt;application-path&gt;\chrome.exe" -- "%1" -- "user-data-dir=D:\Chrome" 3. "C:\&lt;application-path&gt;\chrome.exe" -- "%1 user-data-dir=D:\Chrome"   Conclusively, when I try to open a link from any application, it doesn't open in my current Chrome as a new tab, rather opens a new Chrome window with no plugins and extensions since its from other directory.  Why I have changed my default directory? - because the OS drive was getting low on memory due to heave Chrome caches and apps. In physics sometimes we find energy that is negative. What does the negative sign indicate? I'm currently developing a script for Blender to handle Mesh Frequency Decomposition.  The script is nearly complete, but i need one more thing: The SciPy library to compute eigenvalues and eigenvectors.  Following the installation instructions on , I'm able to install it as well as Numpy. Numpy works fine, but I can't even import SciPy:  Traceback (most recent call last): File "/CAF_FD.py", line 4, in &lt;module&gt; ImportError: No module named 'scipy' Error: Python script fail, look in the console for now...   By the way, I'm working on Linux 64 bit and I've installed SciPy and Numpy with my package manager.  Edit: When I try to use SciPy with a terminal prompt, it works. How do I get started creating an Ubuntu Desktop App? I want to create an Ubuntu desktop app, specifically to replace Gwibber.  I can code in Java, Python and a few other technologies. Adobe Flex would have been an option until Adobe decided to suck some more and stopped support for AIR on Linux.  Note - I don't care about supporting other OS's. It will be a personal Ubuntu specific app. It can I open-source, I don't mind extra help.  It should integrate seamlessly with Ubuntu, notifications and all.  I guess Python it is, is that correct? How do I get started? Why does latex stretch small sections across the whole page vertically? So lets say I have this interface:  public interface IBox {    public void setSize(int size);    public int getSize();    public int getArea();   //...and so on }   And I have a class that implements it:  public class Rectangle implements IBox {    private int size;    //Methods here }   If I wanted to use the interface IBox, i can't actually create an instance of it, in the way:  public static void main(String args[]) {     Ibox myBox=new Ibox(); }   right? So I'd actually have to do this:  public static void main(String args[]) {     Rectangle myBox=new Rectangle(); }   If that's true, then the only purpose of interfaces is to make sure that the class which implements an interface has got the correct methods in it as described by an interface? Or is there any other use of interfaces?