Possibly related to , I noticed a bit ago that occasionally there is an issue with the hats in chat. Here's a screenshot to demonstrate:    As you can see, @AidanMueller's hat is fine in the top image, and is scrunched into the top-right portion of the image in the bottom large one. In the smaller one towards the middle, it seems fine.  As new messages were sent, the issue apparently is only in that one image, here's a picture of the messages sent afterwards:     A quick note: reloading the page does fix the issue:
I have recently noticed that in chat when I type enough and the profile picture expands with my message, the hat stays the same size and it stays in the same place (I have the  app):
Why doesn't 'find' show this file? In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$ Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$.    I'm not sure how to start this proof, if it should be done algebraically or if I should try to use a proof by induction. How can I make a fake name when I use command blocks? I'm trying to make a mini game but I want it so that when you press a button over a command block it will say "BOB welcome", so 'bob' instead of the @a or @p sign and then followed by the message. All I know is that I need to use /tellraw. I was just wondering whether the following statement is correct.  Let R be a ring and M a noetherian R module. Then M is finitely generated. System Load Indicator only shows as a line unless hovered I installed the  GNOME extension on my Ubuntu 18.04, but for some reason, instead of showing a proper graph for CPU usage, it only shows a very thin line that seems to be a small portion of the actual graph. If I hover over it, the proper graph shows. How to make it show the whole graph all the time? What can I do if a package is not available on the newest version of Ubuntu (18.04) but is available on older versions? rake db:migrate doesn't seem to work in production I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework. The problem is stated as follows. Assume we have an infinite tetration as follows $$x^{x^{x^{.^{.^.}}}} \, = \, a$$ With a given $a$ find $x$. The next part of the problem was to discuss the convergence radius of a. If a is too big or too small the tetration does not converge. Below is my humble stab at the problem.  My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius. I) Initial discussion At the start it is obvious that the tetration converges when $a=1$ (just set $x=1$) Now after some computer hardwork it seems that the tetration fails to converge when a is roughly larger than 3. II) Algebraic manipulation $$ x^{x^{x^{.^{.^.}}}} \, = \, a$$ This is the same as $$ x^a \, = \, a$$ $$ \log_a(x^a) \, = \, \log_a(a)$$ $$ \log_a(x) \, = \, \frac{1}{a}$$ $$ x \, = \, a^{\frac{1}{a}}$$ Now, if we let $a=2$ then $x = \sqrt{2}$. After some more computational work, this seems to be correct, which makes me believe this formula is correct. III) Discsussion about convergence By looking at the derivative of $ \displaystyle \large a^{\frac{1}{a}} $ we see that the maxima occurs when $a=e$, which also seems to correspond to the inital computational work. Now I think, that the minima of $\displaystyle \large a^{1/a}$ is zero by looking at its graph, studying its derivative and the endpoints. So that my &quot;guess&quot; or work shows that it converges when $$ a \in [0 \, , \,  1/e] $$ VI) My questions Can my algebraic manipulations be justified? They seem rather sketchy taking the a`th logarithm and so on . (Although they seem to &quot;magically&quot; give out the right answer) By looking at Wikipedia it seems that the tetration converge when $$ a \in \left[ 1/e \, , \, e \right] $$ This is almost what I have, why is my lower bound wrong? How can  I find the correct lower bound? How do you implement Coroutines in C++ shell scripts are still working without #!(sha-bang line) I am new to shell scripts and many books have written that use #!(sha-bang) line in starting of the script to invoke the interpreter .And this will invoke a new shell for script and do the interpretation line by line.But one of my basic script is still running without the magic line.  so my questions are:   from where did my basic script get the interpreter. how did the script manages to locate the interpreter.   now let me tell you about my basic script it just contains the following line:  echo "basic script without the magic lines" Fell for fake sugar daddy. How do I get out? Why do we need multiple approvers for suggested edits? I already have the "Edit Questions And Answers" privilege. Yet, if I approve someone else's edit, I'm told that more votes will be required before the edit is accepted.  This seems a bit peculiar to me, since I could just copy the edited version and paste it myself. Does set difference distribute over set intersection? I am asked to prove that, if $A, B$ and $C$ are sets, then $$A-(B\cap C)=(A-B)\cap(A-C).$$  However, I think that either I have made an error in my working, or the wording of the problem contains a typographical error.    My working so far is as follows: $$\begin{align}x\in(A-(B\cap C)) &amp;\iff (x\in A)\wedge(x\not\in(B\cap C))\\ &amp;\iff(x\in A)\wedge((x\not\in B)\vee(x\not\in C))\\ &amp;\iff((x\in A)\wedge(x\not\in B))\vee((x\in A)\wedge(x\not\in C))\\ &amp;\iff(x\in(A-B))\vee(x\in(A-C))\\ &amp;\iff x\in((A-B)\cup(A-C)) \end{align}$$  First line to second line: by De Morgan's Law. Second line to third line: by distributivity of set intersection over set union. Third line to fourth line: by definitions of intersection and set difference.   If my working is correct, then I have shown that $$A-(B\cap C)=(A-B)\cup(A-C).$$ Am I correct? Are C-style macro names subject to the same naming rules as identifiers?  After a compiler upgrade, it is now emitting this warning for a legacy application:  warning #3649-D: white space is required between the macro name "CHAR_" and its replacement text   #define         CHAR_&amp;        38   This line of code is defining an ASCII value constant for an ampersand.  #define   DOL_SN        36 #define   PERCENT       37 #define   CHAR_&amp;        38 #define   RT_SING       39 #define   LF_PAR        40   I assume that this definition (not actually referenced by any code, as far as I can tell) is buggy and should be changed to something like "CHAR_AMPERSAND"? What was the Historical Precursor for .NET Attributes? What languages or platforms influenced the .NET 1.0 Team to build-in the concept of Attributes from the very start? Was this an Aspect-Oriented thing? Serialization? or something else? I was still in VB6-land at this time, and never used any of the pre-1.0 .NET versions. Why separate Stack Exchange accounts? I understand the reason why Stack Exchange has different sites to separate  from  or . I understand too why the reputation is associated on each site.   Why do I have to create a new  for each web site? I know that when I create a new account, it is automatically associated to my other accounts. But, is there a reason why, when I originally create a user on the first site, I can't go on another site with this user? subcaption vs. subfig: Best package for referencing a subfigure Rename command not found when running a script Registry key / GPO to disable and block Windows 10 upgrade?