This question comprehensively has been edited:Could you think of where or in which situation or condition--or which verbs-- such prepositions could mean the same thing or even interchangeable?  until  by   The documents need to be ready by next Friday.  Here "until" would have the same meaning.   UPDATED: So, you could see both the prepositions has been used with the same verb-- although the meaning of the sentence has been changed. My specific question is about the stative or dynamic verbs, since the preposition "by" could go just along together dynamic verb, and conversely the preposition"until" merely can go with "static" verbs.   Imagine that it takes some time to extend negotiations. Perhaps everybody needs to fill in many forms. There's a lot of administration to do, if you want to extend negotiations. Now look at this sentence:  They decided to extend the negotiations by July 1, 2015. This sentence means that they decided to finish all the administration for the extension before July 1, 2015.  Now look at this sentence:  They decided to extend the negotiations until July 1, 2015. This means that the minimum duration of the negotiations is from now to July 1, 2015. The negotiations will not finish till July 1, 2015.  Thanks in advance
The 10th and last round of negotiations between Iran and the six world powers was held in Vienna in a bid to strike a final deal. However, after the sides failed to agree on a final deal they decided to extend the negotiations until / by July 1, 2015.   In the original text the preposition until has been written. I am, however, wondering if we could use by instead, if so, is there any difference semantically?  Any help would be greatly appreciated
Excel: identifying if all values in a row are not equal Solidify conundrum? I stumbled across a solidify issue, I cannot wrap my head around. I have a simple mesh, consisting of three faces.  When adding a solidify modifier, I expect to get an object with three walls, where every angle is square. However, whatever I try, tweaking the various solidify parameters, what I get is something like the following, with a skewed rim.  Did I hit a bug, or is it a limitation of the solidify modifier? Is there a workaround? How to make crontab email me with output? How can I make crontab email me with the output of its jobs? I have MAILTO=redacted@yahoo.com.au above the jobs, but it doesn't work.  I know I need to use something like Postfix or Sendmail but for the life of me I cannot find out how to achieve this. I've searched and searched for a simple guide on setting up Postfix but they're all insanely complicated and expect you to be setting up a whole server to send and receive email and to know all the terms (like, what is a domain name for outgoing emails?).  All I want to do is have crontab email me. Why is this so difficult??  Additional Info:  My crontab file looks like this:  MAILTO=redacted@yahoo.com.au 1 0 * * * ~/Desktop/toskymesh.sh 59 6 * * * ~/Desktop/tooptus.sh 0 3 * * * snapraid sync   More Additional Info:  The output of ps -ef | grep '[s]endmail'  root 6840 1370 0 10:26 ? 00:00:00 sendmail: MTA: accepting connections   I know for sure cron is working, but I'm testing the mail command with echo Test | mail -s Test redacted@yahoo.com.au anyway. Show that if $g \circ f$ is injective, then so is $f$. The Problem:  Let $X, Y, Z$ be sets and $f: X \to Y, g:Y \to Z$ be functions.  (a) Show that if $g \circ f$ is injective, then so is $f$.  (b) If $g \circ f$ is surjective, must $g$ be surjective?  Where I Am:  So, I really have trouble with these, for some reason. I can draw pictures and make sense of the problems, but writing down proofs is very difficult for me.   Basically, for (a), I ended up with some complicated statement involving an implication implying another implication and then tried to derive a contradiction. It just got so convoluted that I couldn't make sense of it anymore, and I know there's a quick, elegant way to show it.  For (b), I know that $g$ need not be surjective. Once again, though, proving it directly from definitions has given me a bit of a headache.  Any help here would be appreciated. Thanks in advance.  The Proofs!  Ok, I did it. Thanks for the help, everyone! Let me know if there's anything wrong with these proofs, or if they could bet any better.  (a) Suppose $f$ is not injective. Then $$ f(x_1)=f(x_2) \implies x_1 \ne x_2 \text{        }(*).$$ Let $f(x_1)=y_0=f(x_2)$ and let $g(y_0)=z_0$. Then $$ (g \circ f)(x_1) = (g \circ f)(x_2) = g(y_0) = z_0. $$ Since $g \circ f$ is injective, $$ (g \circ f)(x_1) = (g \circ f_2) \implies x_1 = x_2. $$ However, this contradicts $(*)$. Therefore, $f$ must be injective.  (b) Suppose $g$ is not surjective. Then  $$ \forall y \in Y, \exists z \in Z \text{ such that } g(y) \ne z \text{         }(**).$$  Since, $g \circ f$ is surjective,  $$ \forall z \in Z, \exists x \in X \text{ such that } g(f(x)) = z \text{       } (***). $$  Let $f(x) = y$. Then,  $$ g(f(x)) = g(y) = z. $$  Because of $(***)$, this is true for all $z \in Z$, which contradicts $(**)$. Therefore, $g$ must be surjective. l, ls & la -- what are the differences, and are there more of these commands? I tried to use xrandr to set 1680x1050 as a new mode to VGA output, but it says:  sudo xrandr --addmode VGA-0 1680 X Error of failed request:  BadMatch (invalid parameter attributes) Major opcode of failed request:  140 (RANDR) Minor opcode of failed request:  18 (RRAddOutputMode) Serial number of failed request:  35 Current serial number in output stream:  36 Intuitive explanation for density of transformed variable? Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf   $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) &amp; y \ge 0 \\ 0 &amp; y \lt 0\end{cases}$$   I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who doesn't know calculus. In particular, I'm trying to explain why the factor $\frac{1}{\sqrt{y}}$ appears out front. I'll take a stab at it:  Suppose $X$ has a Gaussian distribution. Almost all the weight of its pdf is between the values, say, $-3$ and $3.$ But that maps to 0 to 9 for $Y$. So, the heavy weight in the pdf for $X$ has been extended across a wider range of values in the transformation to $Y$. Thus, for $f_Y(y)$ to be a true pdf the extra heavy weight must be downweighted by the multiplicative factor $\frac{1}{\sqrt{y}}$  How does that sound?  If anyone can provide a better explanation of their own or link to one in a document or textbook I'd greatly appreciate it. I find this variable transformation example in several intro mathematical probability/stats books. But I never find an intuitive explanation with it :( I'm using Emacs with AUCTeX to do all my LaTeX. When it comes to syntax highlighting it seems that all mathematics is by default just orange. Do you know of a mode or package that adds some more fine grained syntax highlighting? For example all commands (\foo), matching braces, sub- and superscripts, etc. should get a different color. I'm writing a custom module for Drupal 8. It defines a field storage configuration object, in a file called modules/mymod/config/install/field.storage.bloom_stem.bs_twitter_ac.yml.  The problem is that this is not removed when I uninstall the module; it is apparently left behind because, when I re-install the module, I get a crash.   drush -y pm-uninstall mymod drush cr drush -y en mymod      exception 'Drupal\Core\Config\PreExistingConfigException' with message 'Configuration objects (field.storage.bloom_stem.bs_twitter_ac) provided by mymod already exist in active configuration'   So it seems I need to some how manually remove this configuration object. Do I need to provide some more code that deletes it when the module is uninstalled? MacBook Pro 2020 Fan Issues I recently purchased a MacBook Pro 2020 13&quot; (1.4 GHz, 8GB Ram, i5). For some reason, when I open Chrome and watch Twitch my computers fans turn on and go crazy. After opening Activity Monitor, I noticed that Google Chrome Helper (Renderer) uses around 50-80% of my CPU. Also, sometimes when I run code on my MacBook Pro, the fans turn on when the program is compiling/running but slow down a few minutes after terminating the program. Also, when watching Twice on Safari, the fans don't come on. However, around 50-60% of the CPU is still being used. Should I be concerned about the CPU usage (I am nervous because I only recently purchased the laptop)? The real fastest gun in the west Are the questions in the about page taken from real posts? If not, who designs them?  Particularly, why does this specific answer have a date from before the question was asked? How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$? How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$? Printing reverse of any String without using any predefined function? Can you teleport farther away with misty step if you have a double from Invoke Duplicity? The Channel Divinity feature says:     you can cast spells as though you were in the illusion's space, but   you must use your own senses. (PHB 63)   If you were where your duplicate is, you could step to a space 30ft from its position. So if it is 60ft from you, you could teleport to a space 90ft from your actual position. But the spell says that:     you teleport up to 30 feet (PHB 260)   This would put a hard limit on the distance you can travel.  Which rule takes precedence here? Source shell script automatically in terminal How can I automatically source a particular shell script when I open a terminal window by right clicking somewhere and choosing "open in terminal"?  For example, every time I open a terminal I need to run the following command line:  source myscript   How can I make it so that I don't have to type this automatically?  My script is written in tsch:  #!/bin/tcsh setenv DISPLAY 127.0.0.1:10.0 cd /ast/dcm/data   I'm using CentOS 7. With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space? Collage of six photos, not Facebook Lookback movie Deep confusion with conventions and signs in geometric optics This is an equation given in my book.     The question is why have they used a negative sign on the LHS?   Now, if you try to derive the mirror equation with simple geometry, you get  1/v +1/u =1/f . I got that equation without applying any signs there!  So what is the need to apply the signs ‘here'?   If i try to derive this equation ( the one in the photo ) i get the exact answer, but with the positive sign in the LHS. WHY we use the negative sign in the derivation, and then  again we use conventions while solving the questions? If HTML, CSS, and Javascript are client-side, why are they components of a PHP file? Ubuntu 18.04 - Dell XPS13 9370 no longer suspends on lid close